diff --git a/applications/test/barycentric/Make/files b/applications/test/barycentric/Make/files
new file mode 100644
index 0000000000..a4628d5cd4
--- /dev/null
+++ b/applications/test/barycentric/Make/files
@@ -0,0 +1,3 @@
+Test-barycentric.C
+
+EXE = $(FOAM_USER_APPBIN)/Test-barycentric
diff --git a/applications/test/barycentric/Make/options b/applications/test/barycentric/Make/options
new file mode 100644
index 0000000000..18e6fe47af
--- /dev/null
+++ b/applications/test/barycentric/Make/options
@@ -0,0 +1,2 @@
+/* EXE_INC = */
+/* EXE_LIBS = */
diff --git a/applications/test/barycentric/Test-barycentric.C b/applications/test/barycentric/Test-barycentric.C
new file mode 100644
index 0000000000..2fbb060a49
--- /dev/null
+++ b/applications/test/barycentric/Test-barycentric.C
@@ -0,0 +1,93 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2022 OpenCFD Ltd.
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+    for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
+
+Application
+    Test-barycentric
+
+Description
+    Some simple tests for barycentric coordinates and transforms
+
+\*---------------------------------------------------------------------------*/
+
+#include "barycentricTensor.H"
+#include "tetrahedron.H"
+#include "vectorField.H"
+#include "IOstreams.H"
+
+using namespace Foam;
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+//  Main program:
+
+int main(int argc, char *argv[])
+{
+    // Tets to test
+    tetPoints tetA
+    (
+        point(0, 0, 0),
+        point(1, 0, 0),
+        point(1, 1, 0),
+        point(1, 1, 1)
+    );
+
+    const barycentricTensor baryT(tetA[0], tetA[1], tetA[2], tetA[3]);
+
+    Info<< nl << "Tet: " << tetA << nl;
+    Info<< "tens:" << baryT << nl;
+
+    for
+    (
+        const barycentric& bary :
+        List<barycentric>
+        ({
+            {0.25, 0.25, 0.25, 0.25},
+            {1, 0, 0, 0},
+            {0, 1, 0, 0},
+            {0, 0, 1, 0},
+            {0, 0, 0, 1},
+            {0, 0, 0, 0}  // Not really valid
+        })
+    )
+    {
+        vector v(tetA.tet().barycentricToPoint(bary));
+        barycentric b(tetA.tet().pointToBarycentric(v));
+
+        Info<< nl
+            << "bary: " << bary << nl
+            << "vec:  " << v << nl
+            // << "Vec:  " << baryT.inner(bary) << nl
+            << "Vec:  " << (baryT & bary) << nl
+            << "bary: " << b << nl
+            // This won't work (needs a differently defined tensor)
+            // << "Bary: " << (v & baryT) << nl
+            ;
+    }
+
+    Info<< "\nEnd\n" << nl;
+
+    return 0;
+}
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
diff --git a/applications/test/momentOfInertia/Test-momentOfInertia.C b/applications/test/momentOfInertia/Test-momentOfInertia.C
index 6af16dbec9..0d5e82286a 100644
--- a/applications/test/momentOfInertia/Test-momentOfInertia.C
+++ b/applications/test/momentOfInertia/Test-momentOfInertia.C
@@ -38,7 +38,7 @@ Description
 #include "polyMesh.H"
 #include "ListOps.H"
 #include "face.H"
-#include "tetPointRef.H"
+#include "tetrahedron.H"
 #include "triFaceList.H"
 #include "OFstream.H"
 #include "meshTools.H"
diff --git a/applications/test/tetTetOverlap/Test-tetTetOverlap.C b/applications/test/tetTetOverlap/Test-tetTetOverlap.C
index 8e770b8a81..0bd390db1d 100644
--- a/applications/test/tetTetOverlap/Test-tetTetOverlap.C
+++ b/applications/test/tetTetOverlap/Test-tetTetOverlap.C
@@ -6,6 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2012-2017 OpenFOAM Foundation
+    Copyright (C) 2022 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -31,7 +32,7 @@ Description
 
 \*---------------------------------------------------------------------------*/
 
-#include "tetPointRef.H"
+#include "tetrahedron.H"
 #include "OFstream.H"
 #include "meshTools.H"
 #include "cut.H"
@@ -44,12 +45,12 @@ void writeOBJ
 (
     Ostream& os,
     label& vertI,
-    const FixedList<point, 4>& tet
+    const tetPoints& tet
 )
 {
-    forAll(tet, fp)
+    for (const point& p : tet)
     {
-        meshTools::writeOBJ(os, tet[fp]);
+        meshTools::writeOBJ(os, p);
     }
     os  << "l " << vertI+1 << ' ' << vertI+2 << nl
         << "l " << vertI+1 << ' ' << vertI+3 << nl
@@ -61,33 +62,27 @@ void writeOBJ
 }
 
 
-tetPointRef makeTetPointRef(const FixedList<point, 4>& p)
-{
-    return tetPointRef(p[0], p[1], p[2], p[3]);
-}
-
-
 int main(int argc, char *argv[])
 {
     // Tets to test
-    FixedList<point, 4> tetA
-    ({
+    tetPoints tetA
+    (
         point(0, 0, 0),
         point(1, 0, 0),
         point(1, 1, 0),
         point(1, 1, 1)
-    });
-    FixedList<point, 4> tetB
-    ({
+    );
+    tetPoints tetB
+    (
         point(0.1, 0.1, 0.1),
         point(1.1, 0.1, 0.1),
         point(1.1, 1.1, 0.1),
         point(1.1, 1.1, 1.1)
-    });
+    );
 
 
     // Do intersection
-    typedef DynamicList<FixedList<point, 4>> tetList;
+    typedef DynamicList<tetPoints> tetList;
     tetList tetsIn1, tetsIn2, tetsOut;
     cut::appendOp<tetList> tetOpIn1(tetsIn1);
     cut::appendOp<tetList> tetOpIn2(tetsIn2);
@@ -155,25 +150,25 @@ int main(int argc, char *argv[])
 
 
     // Check the volumes
-    Info<< "Vol A: " << makeTetPointRef(tetA).mag() << endl;
+    Info<< "Vol A: " << tetA.tet().mag() << endl;
 
     scalar volIn = 0;
-    forAll(tetsIn, i)
+    for (const auto& t : tetsIn)
     {
-        volIn += makeTetPointRef(tetsIn[i]).mag();
+        volIn += t.tet().mag();
     }
     Info<< "Vol A inside B: " << volIn << endl;
 
     scalar volOut = 0;
-    forAll(tetsOut, i)
+    for (const auto& t : tetsOut)
     {
-        volOut += makeTetPointRef(tetsOut[i]).mag();
+        volOut += t.tet().mag();
     }
     Info<< "Vol A outside B: " << volOut << endl;
 
     Info<< "Sum inside and outside: " << volIn + volOut << endl;
 
-    if (mag(volIn + volOut - makeTetPointRef(tetA).mag()) > SMALL)
+    if (mag(volIn + volOut - tetA.tet().mag()) > SMALL)
     {
         FatalErrorInFunction
             << "Tet volumes do not sum up to input tet."
diff --git a/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/cellShapeControl/cellShapeControlMesh/cellShapeControlMesh.C b/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/cellShapeControl/cellShapeControlMesh/cellShapeControlMesh.C
index f1c8d5018c..0277cbfa59 100644
--- a/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/cellShapeControl/cellShapeControlMesh/cellShapeControlMesh.C
+++ b/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/cellShapeControl/cellShapeControlMesh/cellShapeControlMesh.C
@@ -31,7 +31,7 @@ License
 #include "pointIOField.H"
 #include "scalarIOField.H"
 #include "triadIOField.H"
-#include "tetPointRef.H"
+#include "tetrahedron.H"
 #include "plane.H"
 #include "transform.H"
 #include "meshTools.H"
diff --git a/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/cellShapeControl/cellSizeAndAlignmentControl/fileControl/fileControl.C b/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/cellShapeControl/cellSizeAndAlignmentControl/fileControl/fileControl.C
index 9943738775..93381d0b3e 100644
--- a/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/cellShapeControl/cellSizeAndAlignmentControl/fileControl/fileControl.C
+++ b/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/cellShapeControl/cellSizeAndAlignmentControl/fileControl/fileControl.C
@@ -27,7 +27,6 @@ License
 
 #include "fileControl.H"
 #include "addToRunTimeSelectionTable.H"
-#include "tetPointRef.H"
 #include "scalarList.H"
 #include "vectorTools.H"
 #include "pointIOField.H"
@@ -50,9 +49,6 @@ addToRunTimeSelectionTable
 }
 
 
-// * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * * //
-
-
 // * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
 Foam::fileControl::fileControl
diff --git a/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/cellShapeControl/cellSizeAndAlignmentControl/searchableSurfaceControl/searchableSurfaceControl.C b/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/cellShapeControl/cellSizeAndAlignmentControl/searchableSurfaceControl/searchableSurfaceControl.C
index 16edb18b5c..d6c20276f8 100644
--- a/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/cellShapeControl/cellSizeAndAlignmentControl/searchableSurfaceControl/searchableSurfaceControl.C
+++ b/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/cellShapeControl/cellSizeAndAlignmentControl/searchableSurfaceControl/searchableSurfaceControl.C
@@ -31,7 +31,6 @@ License
 #include "cellSizeFunction.H"
 #include "triSurfaceMesh.H"
 #include "searchableBox.H"
-#include "tetPointRef.H"
 #include "vectorTools.H"
 #include "quaternion.H"
 
diff --git a/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/conformalVoronoiMesh/indexedCell/indexedCellChecks.C b/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/conformalVoronoiMesh/indexedCell/indexedCellChecks.C
index 8659e13a2e..b22855935c 100644
--- a/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/conformalVoronoiMesh/indexedCell/indexedCellChecks.C
+++ b/applications/utilities/mesh/generation/foamyMesh/conformalVoronoiMesh/conformalVoronoiMesh/indexedCell/indexedCellChecks.C
@@ -26,7 +26,7 @@ License
 \*---------------------------------------------------------------------------*/
 
 #include "plane.H"
-#include "tetPointRef.H"
+#include "tetrahedron.H"
 #include "pointConversion.H"
 #include "CGALTriangulation3DKernel.H"
 
diff --git a/applications/utilities/mesh/manipulation/checkMesh/writeFields.C b/applications/utilities/mesh/manipulation/checkMesh/writeFields.C
index 7f1f0f3f37..94dccc6712 100644
--- a/applications/utilities/mesh/manipulation/checkMesh/writeFields.C
+++ b/applications/utilities/mesh/manipulation/checkMesh/writeFields.C
@@ -4,7 +4,7 @@
 #include "polyMeshTools.H"
 #include "zeroGradientFvPatchFields.H"
 #include "syncTools.H"
-#include "tetPointRef.H"
+#include "tetrahedron.H"
 #include "regionSplit.H"
 #include "wallDist.H"
 #include "cellAspectRatio.H"
diff --git a/src/OpenFOAM/algorithms/dynamicIndexedOctree/dynamicIndexedOctree.C b/src/OpenFOAM/algorithms/dynamicIndexedOctree/dynamicIndexedOctree.C
index d9fc921789..2998a768db 100644
--- a/src/OpenFOAM/algorithms/dynamicIndexedOctree/dynamicIndexedOctree.C
+++ b/src/OpenFOAM/algorithms/dynamicIndexedOctree/dynamicIndexedOctree.C
@@ -27,7 +27,7 @@ License
 \*---------------------------------------------------------------------------*/
 
 #include "dynamicIndexedOctree.H"
-#include "linePointRef.H"
+#include "line.H"
 #include "OFstream.H"
 #include "ListOps.H"
 
diff --git a/src/OpenFOAM/algorithms/dynamicIndexedOctree/dynamicIndexedOctree.H b/src/OpenFOAM/algorithms/dynamicIndexedOctree/dynamicIndexedOctree.H
index 92e38b62cd..e0277fd2b6 100644
--- a/src/OpenFOAM/algorithms/dynamicIndexedOctree/dynamicIndexedOctree.H
+++ b/src/OpenFOAM/algorithms/dynamicIndexedOctree/dynamicIndexedOctree.H
@@ -35,8 +35,8 @@ SourceFiles
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef dynamicIndexedOctree_H
-#define dynamicIndexedOctree_H
+#ifndef Foam_dynamicIndexedOctree_H
+#define Foam_dynamicIndexedOctree_H
 
 #include "treeBoundBox.H"
 #include "pointIndexHit.H"
@@ -54,7 +54,7 @@ namespace Foam
 
 typedef DynamicList<autoPtr<DynamicList<label>>> contentListList;
 
-// Forward declaration of classes
+// Forward Declarations
 template<class Type> class dynamicIndexedOctree;
 
 template<class Type> Ostream& operator<<
diff --git a/src/OpenFOAM/algorithms/dynamicIndexedOctree/dynamicTreeDataPoint.H b/src/OpenFOAM/algorithms/dynamicIndexedOctree/dynamicTreeDataPoint.H
index 58c797db3d..673f9e14e4 100644
--- a/src/OpenFOAM/algorithms/dynamicIndexedOctree/dynamicTreeDataPoint.H
+++ b/src/OpenFOAM/algorithms/dynamicIndexedOctree/dynamicTreeDataPoint.H
@@ -39,12 +39,12 @@ SourceFiles
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef dynamicTreeDataPoint_H
-#define dynamicTreeDataPoint_H
+#ifndef Foam_dynamicTreeDataPoint_H
+#define Foam_dynamicTreeDataPoint_H
 
 #include "pointField.H"
 #include "treeBoundBox.H"
-#include "linePointRef.H"
+#include "line.H"
 #include "volumeType.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
@@ -52,7 +52,7 @@ SourceFiles
 namespace Foam
 {
 
-// Forward declaration of classes
+// Forward Declarations
 template<class Type> class dynamicIndexedOctree;
 
 /*---------------------------------------------------------------------------*\
diff --git a/src/OpenFOAM/algorithms/indexedOctree/indexedOctree.C b/src/OpenFOAM/algorithms/indexedOctree/indexedOctree.C
index 0111a703a2..a9c99e965d 100644
--- a/src/OpenFOAM/algorithms/indexedOctree/indexedOctree.C
+++ b/src/OpenFOAM/algorithms/indexedOctree/indexedOctree.C
@@ -27,7 +27,7 @@ License
 \*---------------------------------------------------------------------------*/
 
 #include "indexedOctree.H"
-#include "linePointRef.H"
+#include "line.H"
 #include "OFstream.H"
 #include "ListOps.H"
 #include "memInfo.H"
diff --git a/src/OpenFOAM/algorithms/indexedOctree/indexedOctree.H b/src/OpenFOAM/algorithms/indexedOctree/indexedOctree.H
index 05647aa887..13bf6956b2 100644
--- a/src/OpenFOAM/algorithms/indexedOctree/indexedOctree.H
+++ b/src/OpenFOAM/algorithms/indexedOctree/indexedOctree.H
@@ -34,8 +34,8 @@ SourceFiles
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef indexedOctree_H
-#define indexedOctree_H
+#ifndef Foam_indexedOctree_H
+#define Foam_indexedOctree_H
 
 #include "treeBoundBox.H"
 #include "pointIndexHit.H"
@@ -51,7 +51,7 @@ SourceFiles
 namespace Foam
 {
 
-// Forward declaration of classes
+// Forward Declarations
 template<class Type> class indexedOctree;
 template<class Type> Ostream& operator<<(Ostream&, const indexedOctree<Type>&);
 class Istream;
diff --git a/src/OpenFOAM/meshes/meshShapes/cell/cell.C b/src/OpenFOAM/meshes/meshShapes/cell/cell.C
index 293537c85e..2ec1846256 100644
--- a/src/OpenFOAM/meshes/meshShapes/cell/cell.C
+++ b/src/OpenFOAM/meshes/meshShapes/cell/cell.C
@@ -27,7 +27,7 @@ License
 \*---------------------------------------------------------------------------*/
 
 #include "cell.H"
-#include "pyramidPointFaceRef.H"
+#include "pyramid.H"
 
 // * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
 
diff --git a/src/OpenFOAM/meshes/meshShapes/cellModel/cellModel.C b/src/OpenFOAM/meshes/meshShapes/cellModel/cellModel.C
index 926b07abde..da60911c43 100644
--- a/src/OpenFOAM/meshes/meshShapes/cellModel/cellModel.C
+++ b/src/OpenFOAM/meshes/meshShapes/cellModel/cellModel.C
@@ -27,7 +27,7 @@ License
 \*---------------------------------------------------------------------------*/
 
 #include "cellModel.H"
-#include "pyramidPointFaceRef.H"
+#include "pyramid.H"
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
diff --git a/src/OpenFOAM/meshes/meshShapes/edge/edge.H b/src/OpenFOAM/meshes/meshShapes/edge/edge.H
index e029daf60d..a30a723593 100644
--- a/src/OpenFOAM/meshes/meshShapes/edge/edge.H
+++ b/src/OpenFOAM/meshes/meshShapes/edge/edge.H
@@ -45,11 +45,11 @@ SourceFiles
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef edge_H
-#define edge_H
+#ifndef Foam_edge_H
+#define Foam_edge_H
 
 #include "labelPair.H"
-#include "linePointRef.H"
+#include "line.H"
 #include "pointField.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
diff --git a/src/OpenFOAM/meshes/meshShapes/face/face.C b/src/OpenFOAM/meshes/meshShapes/face/face.C
index 0b47dc7000..3a96a556e7 100644
--- a/src/OpenFOAM/meshes/meshShapes/face/face.C
+++ b/src/OpenFOAM/meshes/meshShapes/face/face.C
@@ -28,7 +28,7 @@ License
 
 #include "face.H"
 #include "triFace.H"
-#include "triPointRef.H"
+#include "triangle.H"
 #include "mathematicalConstants.H"
 #include "Circulator.H"
 #include <algorithm>
diff --git a/src/OpenFOAM/meshes/meshShapes/face/face.H b/src/OpenFOAM/meshes/meshShapes/face/face.H
index a3a4776370..1e64cd1881 100644
--- a/src/OpenFOAM/meshes/meshShapes/face/face.H
+++ b/src/OpenFOAM/meshes/meshShapes/face/face.H
@@ -43,8 +43,8 @@ SourceFiles
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef face_H
-#define face_H
+#ifndef Foam_face_H
+#define Foam_face_H
 
 #include "pointField.H"
 #include "labelList.H"
@@ -435,6 +435,12 @@ public:
         static bool sameVertices(const face& a, const face& b);
 
 
+    // Member Operators
+
+        //- Increment (offset) vertices by given amount
+        inline void operator+=(const label vertexOffset);
+
+
     // Hashing
 
         //- The symmetric hash value for face.
@@ -494,19 +500,11 @@ template<> struct Hash<face> : face::hasher {};
 template<>
 struct offsetOp<face>
 {
-    inline face operator()
-    (
-        const face& x,
-        const label offset
-    ) const
+    face operator()(const face& x, const label offset) const
     {
-        face result(x.size());
-
-        forAll(x, i)
-        {
-            result[i] = x[i] + offset;
-        }
-        return result;
+        face f(x);
+        f += offset;
+        return f;
     }
 };
 
diff --git a/src/OpenFOAM/meshes/meshShapes/face/faceI.H b/src/OpenFOAM/meshes/meshShapes/face/faceI.H
index cf500465e3..f9379903c2 100644
--- a/src/OpenFOAM/meshes/meshShapes/face/faceI.H
+++ b/src/OpenFOAM/meshes/meshShapes/face/faceI.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011 OpenFOAM Foundation
-    Copyright (C) 2017-2021 OpenCFD Ltd.
+    Copyright (C) 2017-2022 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -190,6 +190,20 @@ inline Foam::label Foam::face::nTriangles() const
 }
 
 
+// * * * * * * * * * * * * * * * Member Operators  * * * * * * * * * * * * * //
+
+inline void Foam::face::operator+=(const label vertexOffset)
+{
+    if (vertexOffset)
+    {
+        for (label& vrt : static_cast<labelList&>(*this))
+        {
+            vrt += vertexOffset;
+        }
+    }
+}
+
+
 // * * * * * * * * * * * * * * * Global Operators   * * * * * * * * * * * * * //
 
 inline bool Foam::operator==(const face& a, const face& b)
diff --git a/src/OpenFOAM/meshes/meshShapes/face/faceIntersection.C b/src/OpenFOAM/meshes/meshShapes/face/faceIntersection.C
index d338e648e5..b5c00bd97b 100644
--- a/src/OpenFOAM/meshes/meshShapes/face/faceIntersection.C
+++ b/src/OpenFOAM/meshes/meshShapes/face/faceIntersection.C
@@ -27,7 +27,7 @@ License
 
 #include "face.H"
 #include "pointHit.H"
-#include "triPointRef.H"
+#include "triangle.H"
 #include "line.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
diff --git a/src/OpenFOAM/meshes/meshShapes/face/oppositeFace.H b/src/OpenFOAM/meshes/meshShapes/face/oppositeFace.H
index 2907707382..7ed69b1e04 100644
--- a/src/OpenFOAM/meshes/meshShapes/face/oppositeFace.H
+++ b/src/OpenFOAM/meshes/meshShapes/face/oppositeFace.H
@@ -30,13 +30,10 @@ Description
     Class containing opposite face for a prismatic cell with addressing
     and a possibility of failure.
 
-SourceFiles
-    oppositeFace.C
-
 \*---------------------------------------------------------------------------*/
 
-#ifndef oppositeFace_H
-#define oppositeFace_H
+#ifndef Foam_oppositeFace_H
+#define Foam_oppositeFace_H
 
 #include "face.H"
 
@@ -53,7 +50,7 @@ class oppositeFace
 :
     public face
 {
-    // Private data
+    // Private Data
 
         //- Master face index
         const label masterIndex_;
@@ -84,19 +81,19 @@ public:
     // Member Functions
 
         //- Master face index
-        inline label masterIndex() const
+        label masterIndex() const noexcept
         {
             return masterIndex_;
         }
 
-        //- Slave face index
-        inline label oppositeIndex() const
+        //- Opposite face index
+        label oppositeIndex() const noexcept
         {
             return oppositeIndex_;
         }
 
         //- Does the opposite face exist?
-        inline bool found() const
+        bool found() const noexcept
         {
             return oppositeIndex_ >= 0;
         }
diff --git a/src/OpenFOAM/meshes/meshShapes/labelledTri/labelledTri.H b/src/OpenFOAM/meshes/meshShapes/labelledTri/labelledTri.H
index 1295830239..967a876f23 100644
--- a/src/OpenFOAM/meshes/meshShapes/labelledTri/labelledTri.H
+++ b/src/OpenFOAM/meshes/meshShapes/labelledTri/labelledTri.H
@@ -35,8 +35,8 @@ SourceFiles
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef labelledTri_H
-#define labelledTri_H
+#ifndef Foam_labelledTri_H
+#define Foam_labelledTri_H
 
 #include "triFace.H"
 #include "ListListOps.H"
@@ -91,9 +91,9 @@ public:
         //- and optional region index (0 if unspecified)
         inline labelledTri
         (
-            const label a,
-            const label b,
-            const label c,
+            const label p0,
+            const label p1,
+            const label p2,
             const label region = 0
         );
 
@@ -179,13 +179,9 @@ struct offsetOp<labelledTri>
 {
     labelledTri operator()(const labelledTri& x, const label offset) const
     {
-        labelledTri result(x);
-
-        forAll(x, xi)
-        {
-            result[xi] = x[xi] + offset;
-        }
-        return result;
+        labelledTri f(x);
+        f += offset;
+        return f;
     }
 };
 
diff --git a/src/OpenFOAM/meshes/meshShapes/labelledTri/labelledTriI.H b/src/OpenFOAM/meshes/meshShapes/labelledTri/labelledTriI.H
index 84f1671176..8151b6d261 100644
--- a/src/OpenFOAM/meshes/meshShapes/labelledTri/labelledTriI.H
+++ b/src/OpenFOAM/meshes/meshShapes/labelledTri/labelledTriI.H
@@ -77,13 +77,13 @@ inline Foam::labelledTri::labelledTri
 
 inline Foam::labelledTri::labelledTri
 (
-    const label a,
-    const label b,
-    const label c,
+    const label p0,
+    const label p1,
+    const label p2,
     const label region
 )
 :
-    triFace(a, b, c),
+    triFace(p0, p1, p2),
     index_(region)
 {}
 
diff --git a/src/OpenFOAM/meshes/meshShapes/tetCell/tetCell.H b/src/OpenFOAM/meshes/meshShapes/tetCell/tetCell.H
index 9659aac1b5..427fc8bddd 100644
--- a/src/OpenFOAM/meshes/meshShapes/tetCell/tetCell.H
+++ b/src/OpenFOAM/meshes/meshShapes/tetCell/tetCell.H
@@ -40,15 +40,15 @@ SourceFiles
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef tetCell_H
-#define tetCell_H
+#ifndef Foam_tetCell_H
+#define Foam_tetCell_H
 
 #include "FixedList.H"
 #include "triFace.H"
 #include "faceList.H"
 #include "edgeList.H"
 #include "pointField.H"
-#include "tetPointRef.H"
+#include "tetrahedron.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
@@ -85,10 +85,10 @@ public:
         //- Construct from four point labels
         inline tetCell
         (
-            const label a,
-            const label b,
-            const label c,
-            const label d
+            const label p0,
+            const label p1,
+            const label p2,
+            const label p3
         );
 
         //- Construct from an initializer list of four point labels
diff --git a/src/OpenFOAM/meshes/meshShapes/tetCell/tetCellI.H b/src/OpenFOAM/meshes/meshShapes/tetCell/tetCellI.H
index 66f90767ff..d9b0b74502 100644
--- a/src/OpenFOAM/meshes/meshShapes/tetCell/tetCellI.H
+++ b/src/OpenFOAM/meshes/meshShapes/tetCell/tetCellI.H
@@ -36,16 +36,16 @@ inline Foam::tetCell::tetCell()
 
 inline Foam::tetCell::tetCell
 (
-    const label a,
-    const label b,
-    const label c,
-    const label d
+    const label p0,
+    const label p1,
+    const label p2,
+    const label p3
 )
 {
-    operator[](0) = a;
-    operator[](1) = b;
-    operator[](2) = c;
-    operator[](3) = d;
+    operator[](0) = p0;
+    operator[](1) = p1;
+    operator[](2) = p2;
+    operator[](3) = p3;
 }
 
 
diff --git a/src/OpenFOAM/meshes/meshShapes/triFace/triFace.H b/src/OpenFOAM/meshes/meshShapes/triFace/triFace.H
index 28cd39a33f..4444dc9587 100644
--- a/src/OpenFOAM/meshes/meshShapes/triFace/triFace.H
+++ b/src/OpenFOAM/meshes/meshShapes/triFace/triFace.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
-    Copyright (C) 2017-2021 OpenCFD Ltd.
+    Copyright (C) 2017-2022 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -48,7 +48,7 @@ SourceFiles
 #include "pointHit.H"
 #include "intersection.H"
 #include "pointField.H"
-#include "triPointRef.H"
+#include "triangle.H"
 #include "ListListOps.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
@@ -79,12 +79,7 @@ public:
         inline triFace();
 
         //- Construct from three point labels
-        inline triFace
-        (
-            const label a,
-            const label b,
-            const label c
-        );
+        inline triFace(const label p0, const label p1, const label p2);
 
         //- Construct from an initializer list of three point labels
         inline explicit triFace(std::initializer_list<label> list);
@@ -321,6 +316,12 @@ public:
         static inline int compare(const triFace& a, const triFace& b);
 
 
+    // Member Operators
+
+        //- Increment (offset) vertices by given amount
+        inline void operator+=(const label vertexOffset);
+
+
     // Hashing
 
         //- The (commutative) hash value for triFace
@@ -377,19 +378,11 @@ template<> struct Hash<triFace> : triFace::hasher {};
 template<>
 struct offsetOp<triFace>
 {
-    inline triFace operator()
-    (
-        const triFace& x,
-        const label offset
-    ) const
+    triFace operator()(const triFace& x, const label offset) const
     {
-        triFace result;
-
-        forAll(x, i)
-        {
-            result[i] = x[i] + offset;
-        }
-        return result;
+        triFace f(x);
+        f += offset;
+        return f;
     }
 };
 
diff --git a/src/OpenFOAM/meshes/meshShapes/triFace/triFaceI.H b/src/OpenFOAM/meshes/meshShapes/triFace/triFaceI.H
index 15ab7757f8..18e30c7b77 100644
--- a/src/OpenFOAM/meshes/meshShapes/triFace/triFaceI.H
+++ b/src/OpenFOAM/meshes/meshShapes/triFace/triFaceI.H
@@ -28,7 +28,6 @@ License
 
 #include "IOstreams.H"
 #include "face.H"
-#include "triPointRef.H"
 #include <algorithm>  // For std::swap
 
 // * * * * * * * * * * * * * Static Member Functions * * * * * * * * * * * * //
@@ -68,16 +67,11 @@ inline Foam::triFace::triFace()
 {}
 
 
-inline Foam::triFace::triFace
-(
-    const label a,
-    const label b,
-    const label c
-)
+inline Foam::triFace::triFace(const label p0, const label p1, const label p2)
 {
-    operator[](0) = a;
-    operator[](1) = b;
-    operator[](2) = c;
+    operator[](0) = p0;
+    operator[](1) = p1;
+    operator[](2) = p2;
 }
 
 
@@ -476,6 +470,19 @@ inline int Foam::triFace::edgeDirection(const Foam::edge& e) const
 }
 
 
+// * * * * * * * * * * * * * * * Member Operators  * * * * * * * * * * * * * //
+
+inline void Foam::triFace::operator+=(const label vertexOffset)
+{
+    if (vertexOffset)
+    {
+        (*this)[0] += vertexOffset;
+        (*this)[1] += vertexOffset;
+        (*this)[2] += vertexOffset;
+    }
+}
+
+
 // * * * * * * * * * * * * * * * Global Operators  * * * * * * * * * * * * * //
 
 inline bool Foam::operator==(const triFace& a, const triFace& b)
diff --git a/src/OpenFOAM/meshes/polyMesh/polyMeshCheck/polyMeshTools.C b/src/OpenFOAM/meshes/polyMesh/polyMeshCheck/polyMeshTools.C
index 6f03bfb165..51187a0bba 100644
--- a/src/OpenFOAM/meshes/polyMesh/polyMeshCheck/polyMeshTools.C
+++ b/src/OpenFOAM/meshes/polyMesh/polyMeshCheck/polyMeshTools.C
@@ -28,7 +28,7 @@ License
 
 #include "polyMeshTools.H"
 #include "syncTools.H"
-#include "pyramidPointFaceRef.H"
+#include "pyramid.H"
 #include "primitiveMeshTools.H"
 
 // * * * * * * * * * * * * * Static Member Functions * * * * * * * * * * * * //
diff --git a/src/OpenFOAM/meshes/polyMesh/polyMeshTetDecomposition/polyMeshTetDecomposition.H b/src/OpenFOAM/meshes/polyMesh/polyMeshTetDecomposition/polyMeshTetDecomposition.H
index 4cb943eea5..54e415e5ed 100644
--- a/src/OpenFOAM/meshes/polyMesh/polyMeshTetDecomposition/polyMeshTetDecomposition.H
+++ b/src/OpenFOAM/meshes/polyMesh/polyMeshTetDecomposition/polyMeshTetDecomposition.H
@@ -39,13 +39,12 @@ SourceFiles
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef polyMeshTetDecomposition_H
-#define polyMeshTetDecomposition_H
+#ifndef Foam_polyMeshTetDecomposition_H
+#define Foam_polyMeshTetDecomposition_H
 
 #include "polyMesh.H"
 #include "coupledPolyPatch.H"
 #include "syncTools.H"
-#include "tetPointRef.H"
 #include "tetIndices.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
@@ -54,7 +53,7 @@ namespace Foam
 {
 
 /*---------------------------------------------------------------------------*\
-                Class polyMeshTetDecomposition Declaration
+                  Class polyMeshTetDecomposition Declaration
 \*---------------------------------------------------------------------------*/
 
 class polyMeshTetDecomposition
diff --git a/src/OpenFOAM/meshes/polyMesh/polyMeshTetDecomposition/tetIndices.H b/src/OpenFOAM/meshes/polyMesh/polyMeshTetDecomposition/tetIndices.H
index 19a6c23342..883895e863 100644
--- a/src/OpenFOAM/meshes/polyMesh/polyMeshTetDecomposition/tetIndices.H
+++ b/src/OpenFOAM/meshes/polyMesh/polyMeshTetDecomposition/tetIndices.H
@@ -59,8 +59,8 @@ SourceFiles
 #define Foam_tetIndices_H
 
 #include "label.H"
-#include "tetPointRef.H"
-#include "triPointRef.H"
+#include "tetrahedron.H"
+#include "triangle.H"
 #include "polyMesh.H"
 #include "triFace.H"
 #include "face.H"
@@ -76,7 +76,6 @@ class tetIndices;
 Istream& operator>>(Istream&, tetIndices&);
 Ostream& operator<<(Ostream&, const tetIndices&);
 
-
 /*---------------------------------------------------------------------------*\
                          Class tetIndices Declaration
 \*---------------------------------------------------------------------------*/
@@ -149,35 +148,49 @@ public:
         label& tetPt() noexcept { return tetPti_; }
 
 
-    // Searching
+    // Mesh-related
 
-        //- Return the indices corresponding to the tri on the face for
-        //  this tet. The normal of the tri points out of the cell
+        //- The indices corresponding to the tri on the face for this tet.
+        //- The normal of the tri points out of the cell.
         inline triFace faceTriIs
         (
             const polyMesh& mesh,
             const bool warn = true
         ) const;
 
-        //- Return the local indices corresponding to the tri on the face
-        //- for this tet. The normal of the tri points out of the cell
+        //- Local indices corresponding to the tri on the face for this tet.
+        //- The normal of the tri points out of the cell.
         inline triFace triIs
         (
             const polyMesh& mesh,
             const bool warn = true
         ) const;
 
-        //- Return the geometry corresponding to this tet
+
+        //- The tet geometry for this tet,
+        //- where point0 is the cell centre.
         inline tetPointRef tet(const polyMesh& mesh) const;
 
-        //- Return the geometry corresponding to the tri on the face for
-        //- this tet. The normal of the tri points out of the cell
+        //- The tet geometry for this tet (using old positions),
+        //- where point0 is the cell centre.
+        inline tetPointRef oldTet(const polyMesh& mesh) const;
+
+        //- The triangle geometry for the face for this tet.
+        //- The normal of the tri points out of the cell
         inline triPointRef faceTri(const polyMesh& mesh) const;
 
-        //- Return the geometry corresponding to the tri on the face for
-        //- this tet using the old positions
+        //- The triangle geometry for the face for this tet
+        //- (using old positions)
         inline triPointRef oldFaceTri(const polyMesh& mesh) const;
 
+        //- The x/y/z position for given barycentric coordinates
+        //- (where point0 is the cell centre).
+        inline point barycentricToPoint
+        (
+            const polyMesh& mesh,
+            const barycentric& bary
+        ) const;
+
 
     // Other
 
diff --git a/src/OpenFOAM/meshes/polyMesh/polyMeshTetDecomposition/tetIndicesI.H b/src/OpenFOAM/meshes/polyMesh/polyMeshTetDecomposition/tetIndicesI.H
index bda486668c..d7af8fda04 100644
--- a/src/OpenFOAM/meshes/polyMesh/polyMeshTetDecomposition/tetIndicesI.H
+++ b/src/OpenFOAM/meshes/polyMesh/polyMeshTetDecomposition/tetIndicesI.H
@@ -57,9 +57,9 @@ inline Foam::triFace Foam::tetIndices::faceTriIs
     const bool warn
 ) const
 {
-    const Foam::face& f = mesh.faces()[face()];
+    const Foam::face& f = mesh.faces()[facei_];
 
-    label faceBasePtI = mesh.tetBasePtIs()[face()];
+    label faceBasePtI = mesh.tetBasePtIs()[facei_];
 
     if (faceBasePtI < 0)
     {
@@ -67,24 +67,25 @@ inline Foam::triFace Foam::tetIndices::faceTriIs
 
         if (warn && nWarnings_ < maxNWarnings)
         {
-            ++nWarnings_;
             WarningInFunction
-                << "No base point for face " << face() << ", " << f
+                << "No base point for face " << facei_ << ", " << f
                 << ", produces a valid tet decomposition." << endl;
-            if (nWarnings_ == maxNWarnings)
+
+            if (++nWarnings_ == maxNWarnings)
             {
                 Warning
-                    << "Suppressing any further warnings." << endl;
+                    << "Suppressing further warnings." << endl;
             }
         }
     }
 
-    label facePtI = (tetPti_ + faceBasePtI) % f.size();
-    label faceOtherPtI = f.fcIndex(facePtI);
+    const label facePtI = (tetPti_ + faceBasePtI) % f.size();
+    const label faceOtherPtI = f.fcIndex(facePtI);
 
-    if (mesh.faceOwner()[face()] != cell())
+    if (mesh.faceOwner()[facei_] != celli_)
     {
-        std::swap(facePtI, faceOtherPtI);
+        // Neighbour: return flipped face
+        return triFace(f[faceBasePtI], f[faceOtherPtI], f[facePtI]);
     }
 
     return triFace(f[faceBasePtI], f[facePtI], f[faceOtherPtI]);
@@ -97,9 +98,9 @@ inline Foam::triFace Foam::tetIndices::triIs
     const bool warn
 ) const
 {
-    const Foam::face& f = mesh.faces()[face()];
+    const Foam::face& f = mesh.faces()[facei_];
 
-    label faceBasePtI = mesh.tetBasePtIs()[face()];
+    label faceBasePtI = mesh.tetBasePtIs()[facei_];
 
     if (faceBasePtI < 0)
     {
@@ -107,24 +108,25 @@ inline Foam::triFace Foam::tetIndices::triIs
 
         if (warn && nWarnings_ < maxNWarnings)
         {
-            ++nWarnings_;
             WarningInFunction
-                << "No base point for face " << face() << ", " << f
+                << "No base point for face " << facei_ << ", " << f
                 << ", produces a valid tet decomposition." << endl;
-            if (nWarnings_ == maxNWarnings)
+
+            if (++nWarnings_ == maxNWarnings)
             {
                 Warning
-                    << "Suppressing any further warnings." << endl;
+                    << "Suppressing further warnings." << endl;
             }
         }
     }
 
-    label facePtI = (tetPti_ + faceBasePtI) % f.size();
-    label faceOtherPtI = f.fcIndex(facePtI);
+    const label facePtI = (tetPti_ + faceBasePtI) % f.size();
+    const label faceOtherPtI = f.fcIndex(facePtI);
 
-    if (mesh.faceOwner()[face()] != cell())
+    if (mesh.faceOwner()[facei_] != celli_)
     {
-        std::swap(facePtI, faceOtherPtI);
+        // Neighbour: return flipped face
+        return triFace(faceBasePtI, faceOtherPtI, facePtI);
     }
 
     return triFace(faceBasePtI, facePtI, faceOtherPtI);
@@ -133,30 +135,60 @@ inline Foam::triFace Foam::tetIndices::triIs
 
 inline Foam::tetPointRef Foam::tetIndices::tet(const polyMesh& mesh) const
 {
-    const pointField& meshPoints = mesh.points();
+    const pointField& pts = mesh.points();
     const triFace tri = faceTriIs(mesh);
 
     return tetPointRef
     (
-        mesh.cellCentres()[cell()],
-        meshPoints[tri[0]],
-        meshPoints[tri[1]],
-        meshPoints[tri[2]]
+        mesh.cellCentres()[celli_],
+        pts[tri[0]],
+        pts[tri[1]],
+        pts[tri[2]]
+    );
+}
+
+
+inline Foam::tetPointRef Foam::tetIndices::oldTet(const polyMesh& mesh) const
+{
+    const pointField& pts = mesh.oldPoints();
+    const triFace tri = faceTriIs(mesh);
+
+    return tetPointRef
+    (
+        mesh.oldCellCentres()[celli_],
+        pts[tri[0]],
+        pts[tri[1]],
+        pts[tri[2]]
+    );
+}
+
+
+inline Foam::point Foam::tetIndices::barycentricToPoint
+(
+    const polyMesh& mesh,
+    const barycentric& bary
+) const
+{
+    const pointField& pts = mesh.points();
+    const triFace tri = faceTriIs(mesh);
+
+    const point& a = mesh.cellCentres()[celli_];
+    const point& b = pts[tri[0]];
+    const point& c = pts[tri[1]];
+    const point& d = pts[tri[2]];
+
+    return point
+    (
+        (bary.a()*a.x() + bary.b()*b.x() + bary.c()*c.x() + bary.d()*d.x()),
+        (bary.a()*a.y() + bary.b()*b.y() + bary.c()*c.y() + bary.d()*d.y()),
+        (bary.a()*a.z() + bary.b()*b.z() + bary.c()*c.z() + bary.d()*d.z())
     );
 }
 
 
 inline Foam::triPointRef Foam::tetIndices::faceTri(const polyMesh& mesh) const
 {
-    const pointField& meshPoints = mesh.points();
-    const triFace tri = faceTriIs(mesh);
-
-    return triPointRef
-    (
-        meshPoints[tri[0]],
-        meshPoints[tri[1]],
-        meshPoints[tri[2]]
-    );
+    return faceTriIs(mesh).tri(mesh.points());
 }
 
 
@@ -165,15 +197,7 @@ inline Foam::triPointRef Foam::tetIndices::oldFaceTri
     const polyMesh& mesh
 ) const
 {
-    const pointField& meshOldPoints = mesh.oldPoints();
-    const triFace tri = faceTriIs(mesh);
-
-    return triPointRef
-    (
-        meshOldPoints[tri[0]],
-        meshOldPoints[tri[1]],
-        meshOldPoints[tri[2]]
-    );
+    return faceTriIs(mesh).tri(mesh.oldPoints());
 }
 
 
diff --git a/src/OpenFOAM/meshes/primitiveMesh/primitiveMeshCheck/primitiveMeshCheck.C b/src/OpenFOAM/meshes/primitiveMesh/primitiveMeshCheck/primitiveMeshCheck.C
index 96f7e48bda..cce5ed1a5c 100644
--- a/src/OpenFOAM/meshes/primitiveMesh/primitiveMeshCheck/primitiveMeshCheck.C
+++ b/src/OpenFOAM/meshes/primitiveMesh/primitiveMeshCheck/primitiveMeshCheck.C
@@ -27,7 +27,7 @@ License
 \*---------------------------------------------------------------------------*/
 
 #include "primitiveMesh.H"
-#include "pyramidPointFaceRef.H"
+#include "pyramid.H"
 #include "ListOps.H"
 #include "unitConversion.H"
 #include "SortableList.H"
diff --git a/src/OpenFOAM/meshes/primitiveMesh/primitiveMeshCheck/primitiveMeshTools.C b/src/OpenFOAM/meshes/primitiveMesh/primitiveMeshCheck/primitiveMeshTools.C
index a5f93524bf..78c40b4926 100644
--- a/src/OpenFOAM/meshes/primitiveMesh/primitiveMeshCheck/primitiveMeshTools.C
+++ b/src/OpenFOAM/meshes/primitiveMesh/primitiveMeshCheck/primitiveMeshTools.C
@@ -29,7 +29,7 @@ License
 #include "primitiveMeshTools.H"
 #include "primitiveMesh.H"
 #include "syncTools.H"
-#include "pyramidPointFaceRef.H"
+#include "pyramid.H"
 #include "PrecisionAdaptor.H"
 
 // * * * * * * * * * * * * * Static Member Functions * * * * * * * * * * * * //
diff --git a/src/OpenFOAM/meshes/primitiveShapes/cut/cut.H b/src/OpenFOAM/meshes/primitiveShapes/cut/cut.H
index dab54db9e8..7cc6a63077 100644
--- a/src/OpenFOAM/meshes/primitiveShapes/cut/cut.H
+++ b/src/OpenFOAM/meshes/primitiveShapes/cut/cut.H
@@ -33,13 +33,13 @@ SourceFiles
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef cut_H
-#define cut_H
+#ifndef Foam_cut_H
+#define Foam_cut_H
 
 #include "plane.H"
 #include "FixedList.H"
-#include "tetPointRef.H"
-#include "triPointRef.H"
+#include "tetrahedron.H"
+#include "triangle.H"
 #include "zero.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
diff --git a/src/OpenFOAM/meshes/primitiveShapes/line/line.H b/src/OpenFOAM/meshes/primitiveShapes/line/line.H
index f2771a4bc0..e4efe0acbc 100644
--- a/src/OpenFOAM/meshes/primitiveShapes/line/line.H
+++ b/src/OpenFOAM/meshes/primitiveShapes/line/line.H
@@ -35,12 +35,13 @@ SourceFiles
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef line_H
-#define line_H
+#ifndef Foam_line_H
+#define Foam_line_H
 
+#include "point.H"
+#include "point2D.H"
 #include "vector.H"
 #include "PointHit.H"
-#include "point2D.H"
 #include "FixedList.H"
 #include "UList.H"
 
@@ -60,6 +61,12 @@ template<class Point, class PointRef>
 inline Ostream& operator<<(Ostream& os, const line<Point, PointRef>& l);
 
 
+// Common Typedefs
+
+//- A line using referred points
+typedef line<point, const point&> linePointRef;
+
+
 /*---------------------------------------------------------------------------*\
                            Class line Declaration
 \*---------------------------------------------------------------------------*/
@@ -100,19 +107,19 @@ public:
     // Access
 
         //- Return first point
-        inline PointRef first() const noexcept;
+        inline PointRef first() const noexcept { return a_; }
 
         //- Return second (last) point
-        inline PointRef second() const noexcept;
+        inline PointRef second() const noexcept { return b_; }
 
         //- Return last (second) point
-        inline PointRef last() const noexcept;
+        inline PointRef last() const noexcept { return b_; }
 
-        //- Return first point
-        inline PointRef start() const noexcept;
+        //- Return start (first) point
+        inline PointRef start() const noexcept { return a_; }
 
-        //- Return second (last) point
-        inline PointRef end() const noexcept;
+        //- Return end (second) point
+        inline PointRef end() const noexcept { return b_; }
 
 
     // Properties
diff --git a/src/OpenFOAM/meshes/primitiveShapes/line/lineI.H b/src/OpenFOAM/meshes/primitiveShapes/line/lineI.H
index 3ed1e17d45..6a25dfa6f3 100644
--- a/src/OpenFOAM/meshes/primitiveShapes/line/lineI.H
+++ b/src/OpenFOAM/meshes/primitiveShapes/line/lineI.H
@@ -60,40 +60,6 @@ inline Foam::line<Point, PointRef>::line(Istream& is)
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
-template<class Point, class PointRef>
-inline PointRef Foam::line<Point, PointRef>::first() const noexcept
-{
-    return a_;
-}
-
-
-template<class Point, class PointRef>
-inline PointRef Foam::line<Point, PointRef>::second() const noexcept
-{
-    return b_;
-}
-
-
-template<class Point, class PointRef>
-inline PointRef Foam::line<Point, PointRef>::last() const noexcept
-{
-    return b_;
-}
-
-
-template<class Point, class PointRef>
-inline PointRef Foam::line<Point, PointRef>::start() const noexcept
-{
-    return first();
-}
-
-template<class Point, class PointRef>
-inline PointRef Foam::line<Point, PointRef>::end() const noexcept
-{
-    return second();
-}
-
-
 template<class Point, class PointRef>
 inline Point Foam::line<Point, PointRef>::centre() const
 {
diff --git a/src/OpenFOAM/meshes/primitiveShapes/line/linePoint2DRef.H b/src/OpenFOAM/meshes/primitiveShapes/line/linePoint2DRef.H
deleted file mode 100644
index 5422df65c0..0000000000
--- a/src/OpenFOAM/meshes/primitiveShapes/line/linePoint2DRef.H
+++ /dev/null
@@ -1,55 +0,0 @@
-/*---------------------------------------------------------------------------*\
-  =========                 |
-  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
-   \\    /   O peration     |
-    \\  /    A nd           | www.openfoam.com
-     \\/     M anipulation  |
--------------------------------------------------------------------------------
-    Copyright (C) 2011 OpenFOAM Foundation
--------------------------------------------------------------------------------
-License
-    This file is part of OpenFOAM.
-
-    OpenFOAM is free software: you can redistribute it and/or modify it
-    under the terms of the GNU General Public License as published by
-    the Free Software Foundation, either version 3 of the License, or
-    (at your option) any later version.
-
-    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
-    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
-    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
-    for more details.
-
-    You should have received a copy of the GNU General Public License
-    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
-
-Typedef
-    Foam::linePoint2DRef
-
-Description
-    A line using referred 2D points
-
-\*---------------------------------------------------------------------------*/
-
-#ifndef linePoint2DRef_H
-#define linePoint2DRef_H
-
-#include "point2D.H"
-#include "line.H"
-
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-namespace Foam
-{
-
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-typedef line<point2D, const point2D&> linePoint2DRef;
-
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-} // End namespace Foam
-
-#endif
-
-// ************************************************************************* //
diff --git a/src/OpenFOAM/meshes/primitiveShapes/line/linePointRef.H b/src/OpenFOAM/meshes/primitiveShapes/line/linePointRef.H
index fa49276f9e..5661fa432a 100644
--- a/src/OpenFOAM/meshes/primitiveShapes/line/linePointRef.H
+++ b/src/OpenFOAM/meshes/primitiveShapes/line/linePointRef.H
@@ -1,55 +1,11 @@
-/*---------------------------------------------------------------------------*\
-  =========                 |
-  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
-   \\    /   O peration     |
-    \\  /    A nd           | www.openfoam.com
-     \\/     M anipulation  |
--------------------------------------------------------------------------------
-    Copyright (C) 2011 OpenFOAM Foundation
--------------------------------------------------------------------------------
-License
-    This file is part of OpenFOAM.
+// Compatibility include.
+// linePointRef typedef included in line.H (JUL-2022)
 
-    OpenFOAM is free software: you can redistribute it and/or modify it
-    under the terms of the GNU General Public License as published by
-    the Free Software Foundation, either version 3 of the License, or
-    (at your option) any later version.
+#ifndef FoamCompat_linePointRef_H
+#define FoamCompat_linePointRef_H
 
-    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
-    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
-    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
-    for more details.
-
-    You should have received a copy of the GNU General Public License
-    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
-
-Typedef
-    Foam::linePointRef
-
-Description
-    A line using referred points
-
-\*---------------------------------------------------------------------------*/
-
-#ifndef linePointRef_H
-#define linePointRef_H
-
-#include "point.H"
 #include "line.H"
 
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-namespace Foam
-{
-
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-typedef line<point, const point&> linePointRef;
-
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-} // End namespace Foam
-
 #endif
 
 // ************************************************************************* //
diff --git a/src/OpenFOAM/meshes/primitiveShapes/point/point.H b/src/OpenFOAM/meshes/primitiveShapes/point/point.H
index a7adbf82c4..611372d8e9 100644
--- a/src/OpenFOAM/meshes/primitiveShapes/point/point.H
+++ b/src/OpenFOAM/meshes/primitiveShapes/point/point.H
@@ -31,8 +31,8 @@ Description
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef point_H
-#define point_H
+#ifndef Foam_point_H
+#define Foam_point_H
 
 #include "vector.H"
 
diff --git a/src/OpenFOAM/meshes/primitiveShapes/pyramid/pyramid.H b/src/OpenFOAM/meshes/primitiveShapes/pyramid/pyramid.H
index df27fd2444..7ba78bb05d 100644
--- a/src/OpenFOAM/meshes/primitiveShapes/pyramid/pyramid.H
+++ b/src/OpenFOAM/meshes/primitiveShapes/pyramid/pyramid.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011 OpenFOAM Foundation
-    Copyright (C) 2020 OpenCFD Ltd.
+    Copyright (C) 2020-2022 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -37,8 +37,11 @@ SourceFiles
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef pyramid_H
-#define pyramid_H
+#ifndef Foam_pyramid_H
+#define Foam_pyramid_H
+
+#include "point.H"
+#include "face.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
@@ -47,34 +50,39 @@ namespace Foam
 
 // Forward Declarations
 
-template<class Point, class PointRef, class polygonRef>
-class pyramid;
+template<class Point, class PointRef, class PolygonRef> class pyramid;
 
-template<class Point, class PointRef, class polygonRef>
+template<class Point, class PointRef, class PolygonRef>
 inline Istream& operator>>
 (
     Istream& is,
-    pyramid<Point, PointRef, polygonRef>& p
+    pyramid<Point, PointRef, PolygonRef>& p
 );
 
-template<class Point, class PointRef, class polygonRef>
+template<class Point, class PointRef, class PolygonRef>
 inline Ostream& operator<<
 (
     Ostream& os,
-    const pyramid<Point, PointRef, polygonRef>& p
+    const pyramid<Point, PointRef, PolygonRef>& p
 );
 
 
+// Common Typedefs
+
+//- A pyramid using referred point and face
+typedef pyramid<point, const point&, const face&> pyramidPointFaceRef;
+
+
 /*---------------------------------------------------------------------------*\
                            Class pyramid Declaration
 \*---------------------------------------------------------------------------*/
 
-template<class Point, class PointRef, class polygonRef>
+template<class Point, class PointRef, class PolygonRef>
 class pyramid
 {
     // Private Data
 
-        polygonRef base_;
+        PolygonRef base_;
 
         PointRef apex_;
 
@@ -90,7 +98,7 @@ public:
     // Constructors
 
         //- Construct from base polygon and apex point
-        inline pyramid(polygonRef base, const Point& apex);
+        inline pyramid(PolygonRef base, const Point& apex);
 
         //- Construct from Istream
         inline explicit pyramid(Istream& is);
@@ -98,36 +106,36 @@ public:
 
     // Member Functions
 
-        // Access
+    // Access
 
-            //- Return apex point
-            inline const Point& apex() const;
+        //- The apex point
+        const Point& apex() const { return apex_; }
 
-            //- Return base polygon
-            inline polygonRef base() const;
+        //- The base polygon
+        PolygonRef base() const { return base_; }
 
 
-        // Properties
+    // Properties
 
-            //- Return centre (centroid)
-            inline Point centre(const UList<point>& points) const;
+        //- Return centre (centroid)
+        inline Point centre(const UList<point>& points) const;
 
-            //- Return height vector
-            inline vector height(const UList<point>& points) const;
+        //- Return height vector
+        inline vector height(const UList<point>& points) const;
 
-            //- Return scalar magnitude - returns volume of pyramid
-            inline scalar mag(const UList<point>& points) const;
+        //- Return scalar magnitude - returns volume of pyramid
+        inline scalar mag(const UList<point>& points) const;
 
 
     // IOstream Operators
 
-        friend Istream& operator>> <Point, PointRef, polygonRef>
+        friend Istream& operator>> <Point, PointRef, PolygonRef>
         (
             Istream& is,
             pyramid& p
         );
 
-        friend Ostream& operator<< <Point, PointRef, polygonRef>
+        friend Ostream& operator<< <Point, PointRef, PolygonRef>
         (
             Ostream& os,
             const pyramid& p
diff --git a/src/OpenFOAM/meshes/primitiveShapes/pyramid/pyramidI.H b/src/OpenFOAM/meshes/primitiveShapes/pyramid/pyramidI.H
index 145f26baef..d8080c745b 100644
--- a/src/OpenFOAM/meshes/primitiveShapes/pyramid/pyramidI.H
+++ b/src/OpenFOAM/meshes/primitiveShapes/pyramid/pyramidI.H
@@ -29,10 +29,10 @@ License
 
 // * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
-template<class Point, class PointRef, class polygonRef>
-inline Foam::pyramid<Point, PointRef, polygonRef>::pyramid
+template<class Point, class PointRef, class PolygonRef>
+inline Foam::pyramid<Point, PointRef, PolygonRef>::pyramid
 (
-    polygonRef base,
+    PolygonRef base,
     const Point& apex
 )
 :
@@ -41,31 +41,17 @@ inline Foam::pyramid<Point, PointRef, polygonRef>::pyramid
 {}
 
 
-template<class Point, class PointRef, class polygonRef>
-inline Foam::pyramid<Point, PointRef, polygonRef>::pyramid(Istream& is)
+template<class Point, class PointRef, class PolygonRef>
+inline Foam::pyramid<Point, PointRef, PolygonRef>::pyramid(Istream& is)
 {
-    is >> base_ >> apex_;
-    is.check(FUNCTION_NAME);
+    is >> *this;
 }
 
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
-template<class Point, class PointRef, class polygonRef>
-inline const Point& Foam::pyramid<Point, PointRef, polygonRef>::apex() const
-{
-    return apex_;
-}
-
-template<class Point, class PointRef, class polygonRef>
-inline polygonRef Foam::pyramid<Point, PointRef, polygonRef>::base() const
-{
-    return base_;
-}
-
-
-template<class Point, class PointRef, class polygonRef>
-inline Point Foam::pyramid<Point, PointRef, polygonRef>::centre
+template<class Point, class PointRef, class PolygonRef>
+inline Point Foam::pyramid<Point, PointRef, PolygonRef>::centre
 (
     const UList<point>& points
 ) const
@@ -74,8 +60,8 @@ inline Point Foam::pyramid<Point, PointRef, polygonRef>::centre
 }
 
 
-template<class Point, class PointRef, class polygonRef>
-inline Foam::vector Foam::pyramid<Point, PointRef, polygonRef>::height
+template<class Point, class PointRef, class PolygonRef>
+inline Foam::vector Foam::pyramid<Point, PointRef, PolygonRef>::height
 (
     const UList<point>& points
 ) const
@@ -85,8 +71,8 @@ inline Foam::vector Foam::pyramid<Point, PointRef, polygonRef>::height
 }
 
 
-template<class Point, class PointRef, class polygonRef>
-inline Foam::scalar Foam::pyramid<Point, PointRef, polygonRef>::mag
+template<class Point, class PointRef, class PolygonRef>
+inline Foam::scalar Foam::pyramid<Point, PointRef, PolygonRef>::mag
 (
     const UList<point>& points
 ) const
@@ -97,11 +83,11 @@ inline Foam::scalar Foam::pyramid<Point, PointRef, polygonRef>::mag
 
 // * * * * * * * * * * * * * * IOstream Operators  * * * * * * * * * * * * * //
 
-template<class Point, class PointRef, class polygonRef>
+template<class Point, class PointRef, class PolygonRef>
 inline Foam::Istream& Foam::operator>>
 (
     Istream& is,
-    pyramid<Point, PointRef, polygonRef>& p
+    pyramid<Point, PointRef, PolygonRef>& p
 )
 {
     is  >> p.base_ >> p.apex_;
@@ -110,11 +96,11 @@ inline Foam::Istream& Foam::operator>>
 }
 
 
-template<class Point, class PointRef, class polygonRef>
+template<class Point, class PointRef, class PolygonRef>
 inline Foam::Ostream& Foam::operator<<
 (
     Ostream& os,
-    const pyramid<Point, PointRef, polygonRef>& p
+    const pyramid<Point, PointRef, PolygonRef>& p
 )
 {
     os  << p.base_ << tab << p.apex_ << nl;
diff --git a/src/OpenFOAM/meshes/primitiveShapes/pyramid/pyramidPointFaceRef.H b/src/OpenFOAM/meshes/primitiveShapes/pyramid/pyramidPointFaceRef.H
index 638e4d511d..658c8ed904 100644
--- a/src/OpenFOAM/meshes/primitiveShapes/pyramid/pyramidPointFaceRef.H
+++ b/src/OpenFOAM/meshes/primitiveShapes/pyramid/pyramidPointFaceRef.H
@@ -1,56 +1,11 @@
-/*---------------------------------------------------------------------------*\
-  =========                 |
-  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
-   \\    /   O peration     |
-    \\  /    A nd           | www.openfoam.com
-     \\/     M anipulation  |
--------------------------------------------------------------------------------
-    Copyright (C) 2011 OpenFOAM Foundation
--------------------------------------------------------------------------------
-License
-    This file is part of OpenFOAM.
+// Compatibility include
+// pyramidPointFaceRef typedef included in tetrahedron.H (SEP-2017)
 
-    OpenFOAM is free software: you can redistribute it and/or modify it
-    under the terms of the GNU General Public License as published by
-    the Free Software Foundation, either version 3 of the License, or
-    (at your option) any later version.
+#ifndef FoamCompat_pyramidPointFaceRef_H
+#define FoamCompat_pyramidPointFaceRef_H
 
-    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
-    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
-    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
-    for more details.
-
-    You should have received a copy of the GNU General Public License
-    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
-
-Typedef
-    Foam::pyramidPointFaceRef
-
-Description
-    A pyramid using referred points and faces
-
-\*---------------------------------------------------------------------------*/
-
-#ifndef pyramidPointFaceRef_H
-#define pyramidPointFaceRef_H
-
-#include "point.H"
-#include "face.H"
 #include "pyramid.H"
 
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-namespace Foam
-{
-
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-typedef pyramid<point, const point&, const face&> pyramidPointFaceRef;
-
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-} // End namespace Foam
-
 #endif
 
 // ************************************************************************* //
diff --git a/src/OpenFOAM/meshes/primitiveShapes/tetrahedron/tetPointRef.H b/src/OpenFOAM/meshes/primitiveShapes/tetrahedron/tetPointRef.H
index d7405deea8..668bf6fe8c 100644
--- a/src/OpenFOAM/meshes/primitiveShapes/tetrahedron/tetPointRef.H
+++ b/src/OpenFOAM/meshes/primitiveShapes/tetrahedron/tetPointRef.H
@@ -1,55 +1,11 @@
-/*---------------------------------------------------------------------------*\
-  =========                 |
-  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
-   \\    /   O peration     |
-    \\  /    A nd           | www.openfoam.com
-     \\/     M anipulation  |
--------------------------------------------------------------------------------
-    Copyright (C) 2011-2017 OpenFOAM Foundation
--------------------------------------------------------------------------------
-License
-    This file is part of OpenFOAM.
+// Compatibility include.
+// tetPointRef typedef included in tetrahedron.H (SEP-2017)
 
-    OpenFOAM is free software: you can redistribute it and/or modify it
-    under the terms of the GNU General Public License as published by
-    the Free Software Foundation, either version 3 of the License, or
-    (at your option) any later version.
+#ifndef FoamCompat_tetPointRef_H
+#define FoamCompat_tetPointRef_H
 
-    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
-    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
-    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
-    for more details.
-
-    You should have received a copy of the GNU General Public License
-    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
-
-Typedef
-    Foam::tetPointRef
-
-Description
-    A tetrahedron using referred points
-
-\*---------------------------------------------------------------------------*/
-
-#ifndef tetPointRef_H
-#define tetPointRef_H
-
-#include "point.H"
 #include "tetrahedron.H"
 
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-namespace Foam
-{
-
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-typedef tetrahedron<point, const point&> tetPointRef;
-
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-} // End namespace Foam
-
 #endif
 
 // ************************************************************************* //
diff --git a/src/OpenFOAM/meshes/primitiveShapes/tetrahedron/tetPoints.H b/src/OpenFOAM/meshes/primitiveShapes/tetrahedron/tetPoints.H
index ad1127f088..5eeeca360a 100644
--- a/src/OpenFOAM/meshes/primitiveShapes/tetrahedron/tetPoints.H
+++ b/src/OpenFOAM/meshes/primitiveShapes/tetrahedron/tetPoints.H
@@ -1,126 +1,10 @@
-/*---------------------------------------------------------------------------*\
-  =========                 |
-  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
-   \\    /   O peration     |
-    \\  /    A nd           | www.openfoam.com
-     \\/     M anipulation  |
--------------------------------------------------------------------------------
-    Copyright (C) 2011-2012 OpenFOAM Foundation
-    Copyright (C) 2017-2020 OpenCFD Ltd.
--------------------------------------------------------------------------------
-License
-    This file is part of OpenFOAM.
+// Compatibility include.
+// tetPoints defined in tetrahedron.H (JUL-2022)
 
-    OpenFOAM is free software: you can redistribute it and/or modify it
-    under the terms of the GNU General Public License as published by
-    the Free Software Foundation, either version 3 of the License, or
-    (at your option) any later version.
-
-    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
-    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
-    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
-    for more details.
-
-    You should have received a copy of the GNU General Public License
-    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
-
-Class
-    Foam::tetPoints
-
-Description
-    Tet storage. Null constructable (unfortunately tetrahedron<point, point>
-    is not)
-
-SourceFiles
-
-\*---------------------------------------------------------------------------*/
-
-#ifndef tetPoints_H
-#define tetPoints_H
+#ifndef FoamCompat_tetPoints_H
+#define FoamCompat_tetPoints_H
 
 #include "tetrahedron.H"
-#include "FixedList.H"
-#include "treeBoundBox.H"
-
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-namespace Foam
-{
-
-/*---------------------------------------------------------------------------*\
-                         Class tetPoints Declaration
-\*---------------------------------------------------------------------------*/
-
-class tetPoints
-:
-    public FixedList<point, 4>
-{
-public:
-
-    // Constructors
-
-        //- Default construct
-        inline tetPoints()
-        {}
-
-        //- Construct from four points
-        inline tetPoints
-        (
-            const point& a,
-            const point& b,
-            const point& c,
-            const point& d
-        )
-        {
-            operator[](0) = a;
-            operator[](1) = b;
-            operator[](2) = c;
-            operator[](3) = d;
-        }
-
-        //- Copy construct from subset of points
-        inline tetPoints
-        (
-            const UList<point>& points,
-            const FixedList<label, 4>& indices
-        )
-        :
-            FixedList<point, 4>(points, indices)
-        {}
-
-
-    // Member Functions
-
-        //- Return the tetrahedron
-        inline tetPointRef tet() const
-        {
-            return tetPointRef
-            (
-                operator[](0),
-                operator[](1),
-                operator[](2),
-                operator[](3)
-            );
-        }
-
-        //- Calculate the bounding box
-        inline treeBoundBox bounds() const
-        {
-            treeBoundBox bb(operator[](0));
-            for (label i = 1; i < size(); ++i)
-            {
-                bb.add(operator[](i));
-            }
-            return bb;
-        }
-};
-
-
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-} // End namespace Foam
-
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
 #endif
 
diff --git a/src/OpenFOAM/meshes/primitiveShapes/tetrahedron/tetrahedron.C b/src/OpenFOAM/meshes/primitiveShapes/tetrahedron/tetrahedron.C
index 89659e559c..0db8ddd168 100644
--- a/src/OpenFOAM/meshes/primitiveShapes/tetrahedron/tetrahedron.C
+++ b/src/OpenFOAM/meshes/primitiveShapes/tetrahedron/tetrahedron.C
@@ -26,7 +26,6 @@ License
 \*---------------------------------------------------------------------------*/
 
 #include "tetrahedron.H"
-#include "triPointRef.H"
 #include "scalarField.H"
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
diff --git a/src/OpenFOAM/meshes/primitiveShapes/tetrahedron/tetrahedron.H b/src/OpenFOAM/meshes/primitiveShapes/tetrahedron/tetrahedron.H
index 9542ed998a..ae8323f243 100644
--- a/src/OpenFOAM/meshes/primitiveShapes/tetrahedron/tetrahedron.H
+++ b/src/OpenFOAM/meshes/primitiveShapes/tetrahedron/tetrahedron.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
-    Copyright (C) 2018 OpenCFD Ltd.
+    Copyright (C) 2018-2022 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -39,17 +39,17 @@ SourceFiles
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef tetrahedron_H
-#define tetrahedron_H
+#ifndef Foam_tetrahedron_H
+#define Foam_tetrahedron_H
 
 #include "point.H"
-#include "primitiveFieldsFwd.H"
 #include "pointHit.H"
+#include "primitiveFieldsFwd.H"
 #include "Random.H"
 #include "FixedList.H"
 #include "UList.H"
-#include "triPointRef.H"
-#include "boundBox.H"
+#include "triangle.H"
+#include "treeBoundBox.H"
 #include "barycentric.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
@@ -59,28 +59,103 @@ namespace Foam
 
 // Forward Declarations
 class plane;
-class tetPoints;
 
 template<class Point, class PointRef> class tetrahedron;
 
 template<class Point, class PointRef>
-inline Istream& operator>>
-(
-    Istream&,
-    tetrahedron<Point, PointRef>&
-);
+inline Istream& operator>>(Istream&, tetrahedron<Point, PointRef>&);
 
 template<class Point, class PointRef>
-inline Ostream& operator<<
-(
-    Ostream&,
-    const tetrahedron<Point, PointRef>&
-);
+inline Ostream& operator<<(Ostream&, const tetrahedron<Point, PointRef>&);
 
+
+// Common Typedefs
+
+//- A tetrahedron using referred points
 typedef tetrahedron<point, const point&> tetPointRef;
 
+
 /*---------------------------------------------------------------------------*\
-                           class tetrahedron Declaration
+                         Class tetPoints Declaration
+\*---------------------------------------------------------------------------*/
+
+//- Tet point storage. Default constructable (tetrahedron is not)
+class tetPoints
+:
+    public FixedList<point, 4>
+{
+public:
+
+    // Generated Methods
+
+        //- Default construct
+        tetPoints() = default;
+
+
+    // Constructors
+
+        //- Construct from four points
+        inline tetPoints
+        (
+            const point& p0,
+            const point& p1,
+            const point& p2,
+            const point& p3
+        );
+
+        //- Construct from point references
+        inline explicit tetPoints(const tetPointRef& pts);
+
+        //- Construct from four points
+        inline tetPoints(const FixedList<point, 4>& pts);
+
+        //- Copy construct from subset of points
+        inline tetPoints
+        (
+            const UList<point>& points,
+            const FixedList<label, 4>& indices
+        );
+
+
+    // Member Functions
+
+        //- The first vertex
+        const point& a() const { return operator[](0); }
+
+        //- The second vertex
+        const point& b() const { return operator[](1); }
+
+        //- The third vertex
+        const point& c() const { return operator[](2); }
+
+        //- The fourth vertex
+        const point& d() const { return operator[](3); }
+
+        //- The first vertex
+        point& a() { return operator[](0); }
+
+        //- The second vertex
+        point& b() { return operator[](1); }
+
+        //- The third vertex
+        point& c() { return operator[](2); }
+
+        //- The fourth vertex
+        point& d() { return operator[](3); }
+
+        //- Return as tetrahedron reference
+        inline tetPointRef tet() const;
+
+        //- Invert tetrahedron by swapping third and fourth vertices
+        inline void flip();
+
+        //- The bounding box for the tetrahedron
+        inline treeBoundBox bounds() const;
+};
+
+
+/*---------------------------------------------------------------------------*\
+                         Class tetrahedron Declaration
 \*---------------------------------------------------------------------------*/
 
 template<class Point, class PointRef>
@@ -88,7 +163,10 @@ class tetrahedron
 {
 public:
 
-    // Public typedefs
+    // Public Typedefs
+
+        //- The point type
+        typedef Point point_type;
 
         //- Storage type for tets originating from intersecting tets.
         //  (can possibly be smaller than 200)
@@ -130,10 +208,13 @@ public:
 
 private:
 
-    // Private data
+    // Private Data
 
         PointRef a_, b_, c_, d_;
 
+
+    // Private Member Functions
+
         inline static point planeIntersection
         (
             const FixedList<scalar, 4>&,
@@ -161,7 +242,7 @@ private:
 
 public:
 
-    // Member constants
+    // Member Constants
 
         enum
         {
@@ -172,15 +253,18 @@ public:
 
     // Constructors
 
-        //- Construct from points
+        //- Construct from four points
         inline tetrahedron
         (
-            const Point& a,
-            const Point& b,
-            const Point& c,
-            const Point& d
+            const Point& p0,
+            const Point& p1,
+            const Point& p2,
+            const Point& p3
         );
 
+        //- Construct from four points
+        inline tetrahedron(const FixedList<Point, 4>& pts);
+
         //- Construct from four points in the list of points
         inline tetrahedron
         (
@@ -189,24 +273,27 @@ public:
         );
 
         //- Construct from Istream
-        inline tetrahedron(Istream&);
+        inline explicit tetrahedron(Istream&);
 
 
     // Member Functions
 
-        // Access
+    // Access
 
-            //- Return vertices
-            inline const Point& a() const;
+        //- Return vertex a
+        const Point& a() const noexcept { return a_; }
 
-            inline const Point& b() const;
+        //- Return vertex b
+        const Point& b() const noexcept { return b_; }
 
-            inline const Point& c() const;
+        //- Return vertex c
+        const Point& c() const noexcept { return c_; }
 
-            inline const Point& d() const;
+        //- Return vertex d
+        const Point& d() const noexcept { return d_; }
 
-            //- Return i-th face
-            inline triPointRef tri(const label facei) const;
+        //- Return i-th face
+        inline triPointRef tri(const label facei) const;
 
 
         // Properties
@@ -236,12 +323,12 @@ public:
             inline scalar circumRadius() const;
 
             //- Return quality: Ratio of tetrahedron and circum-sphere
-            //  volume, scaled so that a regular tetrahedron has a
-            //  quality of 1
+            //- volume, scaled so that a regular tetrahedron has a
+            //- quality of 1
             inline scalar quality() const;
 
             //- Return a random point in the tetrahedron from a
-            //  uniform distribution
+            //- uniform distribution
             inline Point randomPoint(Random& rndGen) const;
 
             //- Calculate the point from the given barycentric coordinates.
diff --git a/src/OpenFOAM/meshes/primitiveShapes/tetrahedron/tetrahedronI.H b/src/OpenFOAM/meshes/primitiveShapes/tetrahedron/tetrahedronI.H
index f69fd8f707..7613f38048 100644
--- a/src/OpenFOAM/meshes/primitiveShapes/tetrahedron/tetrahedronI.H
+++ b/src/OpenFOAM/meshes/primitiveShapes/tetrahedron/tetrahedronI.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2017 OpenFOAM Foundation
-    Copyright (C) 2018 OpenCFD Ltd.
+    Copyright (C) 2018-2022 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -28,24 +28,76 @@ License
 
 #include "triangle.H"
 #include "IOstreams.H"
-#include "tetPoints.H"
 #include "plane.H"
 
 // * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
+inline Foam::tetPoints::tetPoints
+(
+    const point& p0,
+    const point& p1,
+    const point& p2,
+    const point& p3
+)
+{
+    operator[](0) = p0;
+    operator[](1) = p1;
+    operator[](2) = p2;
+    operator[](3) = p3;
+}
+
+
+inline Foam::tetPoints::tetPoints(const tetPointRef& pts)
+{
+    operator[](0) = pts.a();
+    operator[](1) = pts.b();
+    operator[](2) = pts.c();
+    operator[](3) = pts.d();
+}
+
+
+inline Foam::tetPoints::tetPoints(const FixedList<point, 4>& pts)
+:
+    FixedList<point, 4>(pts)
+{}
+
+
+inline Foam::tetPoints::tetPoints
+(
+    const UList<point>& points,
+    const FixedList<label, 4>& indices
+)
+:
+    FixedList<point, 4>(points, indices)
+{}
+
+
 template<class Point, class PointRef>
 inline Foam::tetrahedron<Point, PointRef>::tetrahedron
 (
-    const Point& a,
-    const Point& b,
-    const Point& c,
-    const Point& d
+    const Point& p0,
+    const Point& p1,
+    const Point& p2,
+    const Point& p3
 )
 :
-    a_(a),
-    b_(b),
-    c_(c),
-    d_(d)
+    a_(p0),
+    b_(p1),
+    c_(p2),
+    d_(p3)
+{}
+
+
+template<class Point, class PointRef>
+inline Foam::tetrahedron<Point, PointRef>::tetrahedron
+(
+    const FixedList<Point, 4>& pts
+)
+:
+    a_(pts[0]),
+    b_(pts[1]),
+    c_(pts[2]),
+    d_(pts[3])
 {}
 
 
@@ -72,33 +124,31 @@ inline Foam::tetrahedron<Point, PointRef>::tetrahedron(Istream& is)
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
-template<class Point, class PointRef>
-inline const Point& Foam::tetrahedron<Point, PointRef>::a() const
+inline Foam::tetPointRef Foam::tetPoints::tet() const
 {
-    return a_;
+    return tetPointRef(a(), b(), c(), d());
 }
 
 
-template<class Point, class PointRef>
-inline const Point& Foam::tetrahedron<Point, PointRef>::b() const
+inline void Foam::tetPoints::flip()
 {
-    return b_;
+    // swap pt2 <-> pt3
+    point t(c());
+    c() = d();
+    d() = t;
 }
 
 
-template<class Point, class PointRef>
-inline const Point& Foam::tetrahedron<Point, PointRef>::c() const
+inline Foam::treeBoundBox Foam::tetPoints::bounds() const
 {
-    return c_;
+    treeBoundBox bb;
+    bb.add(static_cast<const FixedList<point, 4>&>(*this));
+    return bb;
 }
 
 
-template<class Point, class PointRef>
-inline const Point& Foam::tetrahedron<Point, PointRef>::d() const
-{
-    return d_;
-}
-
+// Warning. Ordering of faces needs to be the same for a tetrahedron class,
+// tetrahedron cell shape model and a tetCell
 
 template<class Point, class PointRef>
 inline Foam::triPointRef Foam::tetrahedron<Point, PointRef>::tri
@@ -257,7 +307,7 @@ inline Point Foam::tetrahedron<Point, PointRef>::barycentricToPoint
     const barycentric& bary
 ) const
 {
-    return bary[0]*a_ + bary[1]*b_ + bary[2]*c_ + bary[3]*d_;
+    return Point(bary.a()*a_ + bary.b()*b_ + bary.c()*c_ + bary.d()*d_);
 }
 
 
@@ -310,7 +360,7 @@ inline Foam::scalar Foam::tetrahedron<Point, PointRef>::pointToBarycentric
     bary[0] = res.x();
     bary[1] = res.y();
     bary[2] = res.z();
-    bary[3] = 1 - cmptSum(res);
+    bary[3] = 1 - bary[0] - bary[1] - bary[2];
 
     return detT;
 }
@@ -334,63 +384,83 @@ inline Foam::pointHit Foam::tetrahedron<Point, PointRef>::nearestPoint
 
     bool inside = true;
 
-    if (((p - b_) & Sa()) >= 0)
+    // Side a
     {
-        // p is outside halfspace plane of tri
-        pointHit info = triangle<Point, PointRef>(b_, c_, d_).nearestPoint(p);
+        const triangle<Point, PointRef> tria(b_, c_, d_);
 
-        inside = false;
-
-        if (info.distance() < minOutsideDistance)
+        if (((p - b_) & tria.areaNormal()) >= 0)
         {
-            closestPt = info.rawPoint();
+            // p is outside halfspace plane of tri
+            pointHit info = tria.nearestPoint(p);
 
-            minOutsideDistance = info.distance();
+            inside = false;
+
+            if (info.distance() < minOutsideDistance)
+            {
+                closestPt = info.rawPoint();
+
+                minOutsideDistance = info.distance();
+            }
         }
     }
 
-    if (((p - a_) & Sb()) >= 0)
+    // Side b
     {
-        // p is outside halfspace plane of tri
-        pointHit info = triangle<Point, PointRef>(a_, d_, c_).nearestPoint(p);
+        const triangle<Point, PointRef> tria(a_, d_, c_);
 
-        inside = false;
-
-        if (info.distance() < minOutsideDistance)
+        if (((p - a_) & tria.areaNormal()) >= 0)
         {
-            closestPt = info.rawPoint();
+            // p is outside halfspace plane of tri
+            pointHit info = tria.nearestPoint(p);
 
-            minOutsideDistance = info.distance();
+            inside = false;
+
+            if (info.distance() < minOutsideDistance)
+            {
+                closestPt = info.rawPoint();
+
+                minOutsideDistance = info.distance();
+            }
         }
     }
 
-    if (((p - a_) & Sc()) >= 0)
+    // Side c
     {
-        // p is outside halfspace plane of tri
-        pointHit info = triangle<Point, PointRef>(a_, b_, d_).nearestPoint(p);
+        const triangle<Point, PointRef> tria(a_, b_, d_);
 
-        inside = false;
-
-        if (info.distance() < minOutsideDistance)
+        if (((p - a_) & tria.areaNormal()) >= 0)
         {
-            closestPt = info.rawPoint();
+            // p is outside halfspace plane of tri
+            pointHit info = tria.nearestPoint(p);
 
-            minOutsideDistance = info.distance();
+            inside = false;
+
+            if (info.distance() < minOutsideDistance)
+            {
+                closestPt = info.rawPoint();
+
+                minOutsideDistance = info.distance();
+            }
         }
     }
 
-    if (((p - a_) & Sd()) >= 0)
+    // Side c
     {
-        // p is outside halfspace plane of tri
-        pointHit info = triangle<Point, PointRef>(a_, c_, b_).nearestPoint(p);
+        const triangle<Point, PointRef> tria(a_, c_, b_);
 
-        inside = false;
-
-        if (info.distance() < minOutsideDistance)
+        if (((p - a_) & tria.areaNormal()) >= 0)
         {
-            closestPt = info.rawPoint();
+            // p is outside halfspace plane of tri
+            pointHit info = tria.nearestPoint(p);
 
-            minOutsideDistance = info.distance();
+            inside = false;
+
+            if (info.distance() < minOutsideDistance)
+            {
+                closestPt = info.rawPoint();
+
+                minOutsideDistance = info.distance();
+            }
         }
     }
 
@@ -412,7 +482,7 @@ inline Foam::pointHit Foam::tetrahedron<Point, PointRef>::nearestPoint
 
 
 template<class Point, class PointRef>
-bool Foam::tetrahedron<Point, PointRef>::inside(const point& pt) const
+bool Foam::tetrahedron<Point, PointRef>::inside(const point& p) const
 {
     // For robustness, assuming that the point is in the tet unless
     // "definitively" shown otherwise by obtaining a positive dot
@@ -429,55 +499,41 @@ bool Foam::tetrahedron<Point, PointRef>::inside(const point& pt) const
     // planeBase[2] = tetBasePt = b_
     // planeBase[3] = tetBasePt = b_
 
-    vector n = Zero;
-
+    // Side a
     {
-        // 0, a
-        const point& basePt = b_;
+        const triangle<Point, PointRef> tria(b_, c_, d_);
 
-        n = Sa();
-        n /= (Foam::mag(n) + VSMALL);
-
-        if (((pt - basePt) & n) > SMALL)
+        if (((p - b_) & tria.unitNormal()) > SMALL)
         {
             return false;
         }
     }
 
+    // Side b
     {
-        // 1, b
-        const point& basePt = c_;
+        const triangle<Point, PointRef> tria(a_, d_, c_);
 
-        n = Sb();
-        n /= (Foam::mag(n) + VSMALL);
-
-        if (((pt - basePt) & n) > SMALL)
+        if (((p - a_) & tria.unitNormal()) > SMALL)
         {
             return false;
         }
     }
 
+    // Side c
     {
-        // 2, c
-        const point& basePt = b_;
+        const triangle<Point, PointRef> tria(a_, b_, d_);
 
-        n = Sc();
-        n /= (Foam::mag(n) + VSMALL);
-
-        if (((pt - basePt) & n) > SMALL)
+        if (((p - a_) & tria.unitNormal()) > SMALL)
         {
             return false;
         }
     }
 
+    // Side d
     {
-        // 3, d
-        const point& basePt = b_;
+        const triangle<Point, PointRef> tria(a_, c_, b_);
 
-        n = Sd();
-        n /= (Foam::mag(n) + VSMALL);
-
-        if (((pt - basePt) & n) > SMALL)
+        if (((p - a_) & tria.unitNormal()) > SMALL)
         {
             return false;
         }
@@ -1055,6 +1111,7 @@ inline Foam::Ostream& Foam::operator<<
     const tetrahedron<Point, PointRef>& t
 )
 {
+    // Format like FixedList
     os  << nl
         << token::BEGIN_LIST
         << t.a_ << token::SPACE
diff --git a/src/OpenFOAM/meshes/primitiveShapes/triangle/triPointRef.H b/src/OpenFOAM/meshes/primitiveShapes/triangle/triPointRef.H
index 5aba23926e..7248f2eac7 100644
--- a/src/OpenFOAM/meshes/primitiveShapes/triangle/triPointRef.H
+++ b/src/OpenFOAM/meshes/primitiveShapes/triangle/triPointRef.H
@@ -1,55 +1,11 @@
-/*---------------------------------------------------------------------------*\
-  =========                 |
-  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
-   \\    /   O peration     |
-    \\  /    A nd           | www.openfoam.com
-     \\/     M anipulation  |
--------------------------------------------------------------------------------
-    Copyright (C) 2011 OpenFOAM Foundation
--------------------------------------------------------------------------------
-License
-    This file is part of OpenFOAM.
+// Compatibility include.
+// triPointRef typedef included in triangle.H (NOV-2015)
 
-    OpenFOAM is free software: you can redistribute it and/or modify it
-    under the terms of the GNU General Public License as published by
-    the Free Software Foundation, either version 3 of the License, or
-    (at your option) any later version.
+#ifndef FoamCompat_triPointRef_H
+#define FoamCompat_triPointRef_H
 
-    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
-    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
-    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
-    for more details.
-
-    You should have received a copy of the GNU General Public License
-    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
-
-Typedef
-    Foam::triPointRef
-
-Description
-    A triangle using referred points
-
-\*---------------------------------------------------------------------------*/
-
-#ifndef triPointRef_H
-#define triPointRef_H
-
-#include "point.H"
 #include "triangle.H"
 
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-namespace Foam
-{
-
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-typedef triangle<point, const point&> triPointRef;
-
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-} // End namespace Foam
-
 #endif
 
 // ************************************************************************* //
diff --git a/src/OpenFOAM/meshes/primitiveShapes/triangle/triPoints.H b/src/OpenFOAM/meshes/primitiveShapes/triangle/triPoints.H
index 704ac27610..e6ec1e63e0 100644
--- a/src/OpenFOAM/meshes/primitiveShapes/triangle/triPoints.H
+++ b/src/OpenFOAM/meshes/primitiveShapes/triangle/triPoints.H
@@ -1,111 +1,10 @@
-/*---------------------------------------------------------------------------*\
-  =========                 |
-  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
-   \\    /   O peration     |
-    \\  /    A nd           | www.openfoam.com
-     \\/     M anipulation  |
--------------------------------------------------------------------------------
-    Copyright (C) 2015 OpenFOAM Foundation
-    Copyright (C) 2017-2020 OpenCFD Ltd.
--------------------------------------------------------------------------------
-License
-    This file is part of OpenFOAM.
+// Compatibility include.
+// triPoints defined in triangle.H (JUL-2022)
 
-    OpenFOAM is free software: you can redistribute it and/or modify it
-    under the terms of the GNU General Public License as published by
-    the Free Software Foundation, either version 3 of the License, or
-    (at your option) any later version.
+#ifndef FoamCompat_triPoints_H
+#define FoamCompat_triPoints_H
 
-    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
-    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
-    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
-    for more details.
-
-    You should have received a copy of the GNU General Public License
-    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
-
-Class
-    Foam::triPoints
-
-Description
-    Triangle storage. Null constructable (unfortunately triangle<point, point>
-    is not)
-
-SourceFiles
-
-\*---------------------------------------------------------------------------*/
-
-#ifndef triPoints_H
-#define triPoints_H
-
-#include "FixedList.H"
-#include "treeBoundBox.H"
-
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-namespace Foam
-{
-
-/*---------------------------------------------------------------------------*\
-                          Class triPoints Declaration
-\*---------------------------------------------------------------------------*/
-
-class triPoints
-:
-    public FixedList<point, 3>
-{
-public:
-
-    // Constructors
-
-        //- Default construct
-        inline triPoints()
-        {}
-
-        //- Construct from points
-        inline triPoints
-        (
-            const point& a,
-            const point& b,
-            const point& c
-        )
-        {
-            operator[](0) = a;
-            operator[](1) = b;
-            operator[](2) = c;
-        }
-
-        //- Copy construct from subset of points
-        inline triPoints
-        (
-            const UList<point>& points,
-            const FixedList<label, 3>& indices
-        )
-        :
-            FixedList<point, 3>(points, indices)
-        {}
-
-
-    // Member Functions
-
-        //- Calculate the bounding box
-        inline treeBoundBox bounds() const
-        {
-            treeBoundBox bb(operator[](0));
-            for (label i = 1; i < size(); ++i)
-            {
-                bb.add(operator[](i));
-            }
-            return bb;
-        }
-};
-
-
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-} // End namespace Foam
-
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+#include "triangle.H"
 
 #endif
 
diff --git a/src/OpenFOAM/meshes/primitiveShapes/triangle/triangle.C b/src/OpenFOAM/meshes/primitiveShapes/triangle/triangle.C
index ef3e90a830..277db1800c 100644
--- a/src/OpenFOAM/meshes/primitiveShapes/triangle/triangle.C
+++ b/src/OpenFOAM/meshes/primitiveShapes/triangle/triangle.C
@@ -26,7 +26,6 @@ License
 \*---------------------------------------------------------------------------*/
 
 #include "triangle.H"
-#include "triPoints.H"
 #include "plane.H"
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
diff --git a/src/OpenFOAM/meshes/primitiveShapes/triangle/triangle.H b/src/OpenFOAM/meshes/primitiveShapes/triangle/triangle.H
index b25ccf8724..6f1ed0a1ae 100644
--- a/src/OpenFOAM/meshes/primitiveShapes/triangle/triangle.H
+++ b/src/OpenFOAM/meshes/primitiveShapes/triangle/triangle.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2017 OpenFOAM Foundation
-    Copyright (C) 2018-2020 OpenCFD Ltd.
+    Copyright (C) 2018-2022 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -35,18 +35,20 @@ SourceFiles
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef triangle_H
-#define triangle_H
+#ifndef Foam_triangle_H
+#define Foam_triangle_H
 
 #include "intersection.H"
+#include "point.H"
 #include "vector.H"
 #include "tensor.H"
 #include "pointHit.H"
 #include "Random.H"
 #include "FixedList.H"
 #include "UList.H"
-#include "linePointRef.H"
+#include "line.H"
 #include "barycentric2D.H"
+#include "treeBoundBox.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
@@ -55,7 +57,6 @@ namespace Foam
 
 // Forward Declarations
 class plane;
-class triPoints;
 
 template<class Point, class PointRef> class triangle;
 
@@ -72,6 +73,73 @@ inline Ostream& operator<<(Ostream&, const triangle<Point, PointRef>&);
 typedef triangle<point, const point&> triPointRef;
 
 
+/*---------------------------------------------------------------------------*\
+                          Class triPoints Declaration
+\*---------------------------------------------------------------------------*/
+
+//- Triangle point storage. Default constructable (triangle is not)
+class triPoints
+:
+    public FixedList<point, 3>
+{
+public:
+
+    // Generated Methods
+
+        //- Default construct
+        triPoints() = default;
+
+
+    // Constructors
+
+        //- Construct from three points
+        inline triPoints(const point& p0, const point& p1, const point& p2);
+
+        //- Construct from point references
+        inline explicit triPoints(const triPointRef& pts);
+
+        //- Construct from three points
+        inline triPoints(const FixedList<point, 3>& pts);
+
+        //- Copy construct from subset of points
+        inline triPoints
+        (
+            const UList<point>& points,
+            const FixedList<label, 3>& indices
+        );
+
+
+    // Member Functions
+
+        //- The first vertex
+        const point& a() const { return operator[](0); }
+
+        //- The second vertex
+        const point& b() const { return operator[](1); }
+
+        //- The third vertex
+        const point& c() const { return operator[](2); }
+
+        //- The first vertex
+        point& a() { return operator[](0); }
+
+        //- The second vertex
+        point& b() { return operator[](1); }
+
+        //- The third vertex
+        point& c() { return operator[](2); }
+
+        //- Return as triangle reference
+        inline triPointRef tri() const;
+
+        //- Flip triangle orientation by swapping second and third vertices
+        inline void flip();
+
+        //- The bounding box for the tetrahedron
+        inline treeBoundBox bounds() const;
+};
+
+
 /*---------------------------------------------------------------------------*\
                           Class triangle Declaration
 \*---------------------------------------------------------------------------*/
@@ -90,7 +158,7 @@ public:
         //- with another triangle
         typedef FixedList<triPoints, 27> triIntersectionList;
 
-        //- The proximity classifications
+        //- Proximity classifications
         enum proxType
         {
             NONE = 0,   //!< Unknown proximity
@@ -99,10 +167,10 @@ public:
         };
 
 
-    // Public classes
+    // Public Classes
 
-        // Classes for use in sliceWithPlane. What to do with decomposition
-        // of triangle.
+        // Classes for use in sliceWithPlane.
+        // What to do with decomposition of triangle.
 
             //- Dummy
             class dummyOp
@@ -169,10 +237,10 @@ public:
     // Constructors
 
         //- Construct from three points
-        inline triangle(const Point& a, const Point& b, const Point& c);
+        inline triangle(const Point& p0, const Point& p1, const Point& p2);
 
         //- Construct from three points
-        inline triangle(const FixedList<Point, 3>& tri);
+        inline triangle(const FixedList<Point, 3>& pts);
 
         //- Construct from three points in the list of points
         //  The indices could be from triFace etc.
@@ -188,16 +256,16 @@ public:
 
     // Member Functions
 
-        // Access
+    // Access
 
-            //- Return first vertex
-            inline const Point& a() const;
+        //- The first vertex
+        const Point& a() const noexcept { return a_; }
 
-            //- Return second vertex
-            inline const Point& b() const;
+        //- The second vertex
+        const Point& b() const noexcept { return b_; }
 
-            //- Return third vertex
-            inline const Point& c() const;
+        //- The third vertex
+        const Point& c() const noexcept { return c_; }
 
 
         // Properties
@@ -245,7 +313,7 @@ public:
             ) const;
 
             //- Return a random point on the triangle from a uniform
-            //  distribution
+            //- distribution
             inline Point randomPoint(Random& rndGen) const;
 
             //- Calculate the point from the given barycentric coordinates.
diff --git a/src/OpenFOAM/meshes/primitiveShapes/triangle/triangleI.H b/src/OpenFOAM/meshes/primitiveShapes/triangle/triangleI.H
index 8b2c99f17d..8e20ec1e76 100644
--- a/src/OpenFOAM/meshes/primitiveShapes/triangle/triangleI.H
+++ b/src/OpenFOAM/meshes/primitiveShapes/triangle/triangleI.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2017 OpenFOAM Foundation
-    Copyright (C) 2018 OpenCFD Ltd.
+    Copyright (C) 2018-2022 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -28,34 +28,70 @@ License
 
 #include "IOstreams.H"
 #include "pointHit.H"
-#include "triPoints.H"
 #include "mathematicalConstants.H"
 
 // * * * * * * * * * * * * * * * * Constructors * * * * * * * * * * * * * * //
 
-template<class Point, class PointRef>
-inline Foam::triangle<Point, PointRef>::triangle
+inline Foam::triPoints::triPoints
 (
-    const Point& a,
-    const Point& b,
-    const Point& c
+    const point& p0,
+    const point& p1,
+    const point& p2
+)
+{
+    operator[](0) = p0;
+    operator[](1) = p1;
+    operator[](2) = p2;
+}
+
+
+inline Foam::triPoints::triPoints(const triPointRef& pts)
+{
+    operator[](0) = pts.a();
+    operator[](1) = pts.b();
+    operator[](2) = pts.c();
+}
+
+
+inline Foam::triPoints::triPoints(const FixedList<point, 3>& pts)
+:
+    FixedList<point, 3>(pts)
+{}
+
+
+inline Foam::triPoints::triPoints
+(
+    const UList<point>& points,
+    const FixedList<label, 3>& indices
 )
 :
-    a_(a),
-    b_(b),
-    c_(c)
+    FixedList<point, 3>(points, indices)
 {}
 
 
 template<class Point, class PointRef>
 inline Foam::triangle<Point, PointRef>::triangle
 (
-    const FixedList<Point, 3>& tri
+    const Point& p0,
+    const Point& p1,
+    const Point& p2
 )
 :
-    a_(tri[0]),
-    b_(tri[1]),
-    c_(tri[2])
+    a_(p0),
+    b_(p1),
+    c_(p2)
+{}
+
+
+template<class Point, class PointRef>
+inline Foam::triangle<Point, PointRef>::triangle
+(
+    const FixedList<Point, 3>& pts
+)
+:
+    a_(pts[0]),
+    b_(pts[1]),
+    c_(pts[2])
 {}
 
 
@@ -72,7 +108,6 @@ inline Foam::triangle<Point, PointRef>::triangle
 {}
 
 
-
 template<class Point, class PointRef>
 inline Foam::triangle<Point, PointRef>::triangle(Istream& is)
 {
@@ -82,22 +117,26 @@ inline Foam::triangle<Point, PointRef>::triangle(Istream& is)
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
-template<class Point, class PointRef>
-inline const Point& Foam::triangle<Point, PointRef>::a() const
+inline Foam::triPointRef Foam::triPoints::tri() const
 {
-    return a_;
+    return triPointRef(a(), b(), c());
 }
 
-template<class Point, class PointRef>
-inline const Point& Foam::triangle<Point, PointRef>::b() const
+
+inline void Foam::triPoints::flip()
 {
-    return b_;
+    // swap pt1 <-> pt2
+    point t(b());
+    b() = c();
+    c() = t;
 }
 
-template<class Point, class PointRef>
-inline const Point& Foam::triangle<Point, PointRef>::c() const
+
+inline Foam::treeBoundBox Foam::triPoints::bounds() const
 {
-    return c_;
+    treeBoundBox bb;
+    bb.add(static_cast<const FixedList<point, 3>&>(*this));
+    return bb;
 }
 
 
@@ -916,6 +955,7 @@ inline Foam::Ostream& Foam::operator<<
     const triangle<Point, PointRef>& t
 )
 {
+    // Format like FixedList
     os  << nl
         << token::BEGIN_LIST
         << t.a_ << token::SPACE
diff --git a/src/OpenFOAM/primitives/Barycentric/Barycentric.H b/src/OpenFOAM/primitives/Barycentric/Barycentric.H
index 4112a157e4..bc5da91964 100644
--- a/src/OpenFOAM/primitives/Barycentric/Barycentric.H
+++ b/src/OpenFOAM/primitives/Barycentric/Barycentric.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2016-2017 OpenFOAM Foundation
-    Copyright (C) 2019-2020 OpenCFD Ltd.
+    Copyright (C) 2019-2022 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -28,16 +28,16 @@ Class
     Foam::Barycentric
 
 Description
-    Templated 3D Barycentric derived from VectorSpace. Has 4 components, one of
-    which is redundant.
+    Templated 3D Barycentric derived from VectorSpace.
+    Has 4 components, one of which is redundant.
 
 SourceFiles
     BarycentricI.H
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef Barycentric_H
-#define Barycentric_H
+#ifndef Foam_Barycentric_H
+#define Foam_Barycentric_H
 
 #include "contiguous.H"
 #include "VectorSpace.H"
@@ -74,7 +74,7 @@ public:
     enum components { A, B, C, D };
 
 
-    // Generated Methods
+    // Generated Methods: copy construct/assignment
 
         //- Default construct
         Barycentric() = default;
@@ -94,20 +94,29 @@ public:
             const Cmpt& vd
         );
 
+        //- Construct from three components, calculate fourth component
+        inline Barycentric(const Cmpt& va, const Cmpt& vb, const Cmpt& vc);
+
 
     // Member Functions
 
-        // Access
+    // Component access
 
-            inline const Cmpt& a() const;
-            inline const Cmpt& b() const;
-            inline const Cmpt& c() const;
-            inline const Cmpt& d() const;
+        inline const Cmpt& a() const;
+        inline const Cmpt& b() const;
+        inline const Cmpt& c() const;
+        inline const Cmpt& d() const;
 
-            inline Cmpt& a();
-            inline Cmpt& b();
-            inline Cmpt& c();
-            inline Cmpt& d();
+        inline Cmpt& a();
+        inline Cmpt& b();
+        inline Cmpt& c();
+        inline Cmpt& d();
+
+
+    // Operations
+
+        //- Scalar-product of \c this with another Barycentric.
+        inline Cmpt inner(const Barycentric<Cmpt>& b2) const;
 };
 
 
diff --git a/src/OpenFOAM/primitives/Barycentric/BarycentricI.H b/src/OpenFOAM/primitives/Barycentric/BarycentricI.H
index 11657058c8..dfaf973de7 100644
--- a/src/OpenFOAM/primitives/Barycentric/BarycentricI.H
+++ b/src/OpenFOAM/primitives/Barycentric/BarycentricI.H
@@ -6,6 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2016-2017 OpenFOAM Foundation
+    Copyright (C) 2022 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -50,6 +51,18 @@ inline Foam::Barycentric<Cmpt>::Barycentric
 }
 
 
+template<class Cmpt>
+inline Foam::Barycentric<Cmpt>::Barycentric
+(
+    const Cmpt& va,
+    const Cmpt& vb,
+    const Cmpt& vc
+)
+:
+    Barycentric<Cmpt>(va, vb, vc, (pTraits<Cmpt>::one - va - vb - vc))
+{}
+
+
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
 template<class Cmpt>
@@ -108,6 +121,17 @@ inline Cmpt& Foam::Barycentric<Cmpt>::d()
 }
 
 
+// * * * * * * * * * * * * * * * Member Operations * * * * * * * * * * * * * //
+
+template<class Cmpt>
+inline Cmpt Foam::Barycentric<Cmpt>::inner(const Barycentric<Cmpt>& b2) const
+{
+    const Barycentric<Cmpt>& b1 = *this;
+
+    return (b1.a()*b2.a() + b1.b()*b2.b() + b1.c()*b2.c() + b1.d()*b2.d());
+}
+
+
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
 namespace Foam
@@ -118,7 +142,7 @@ namespace Foam
 template<class Cmpt>
 inline Cmpt operator&(const Barycentric<Cmpt>& b1, const Barycentric<Cmpt>& b2)
 {
-    return b1.a()*b2.a() + b1.b()*b2.b() + b1.c()*b2.c() + b1.d()*b2.d();
+    return b1.inner(b2);
 }
 
 
diff --git a/src/OpenFOAM/primitives/Barycentric/BarycentricTensor.H b/src/OpenFOAM/primitives/Barycentric/BarycentricTensor.H
index d16ecf0d51..ceaa29f01a 100644
--- a/src/OpenFOAM/primitives/Barycentric/BarycentricTensor.H
+++ b/src/OpenFOAM/primitives/Barycentric/BarycentricTensor.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2017 OpenFOAM Foundation
-    Copyright (C) 2019-2020 OpenCFD Ltd.
+    Copyright (C) 2019-2022 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -28,18 +28,17 @@ Class
     Foam::BarycentricTensor
 
 Description
-    Templated 4x3 tensor derived from VectorSpace. Has 12 components. Can
-    represent a barycentric transformation as a matrix-barycentric inner-
-    product. Can alternatively represent an inverse barycentric transformation
-    as a vector-matrix inner-product.
+    Templated 4x3 tensor derived from VectorSpace. Has 12 components.
+    Can represent a barycentric transformation as a matrix-barycentric
+    inner-product.
 
 SourceFiles
     BarycentricTensorI.H
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef BarycentricTensor_H
-#define BarycentricTensor_H
+#ifndef Foam_BarycentricTensor_H
+#define Foam_BarycentricTensor_H
 
 #include "Barycentric.H"
 #include "Tensor.H"
@@ -64,7 +63,8 @@ public:
     // Typedefs
 
         //- Equivalent type of labels used for valid component indexing
-        typedef Tensor<label> labelType;
+        //- (unused)
+        typedef BarycentricTensor<label> labelType;
 
 
     // Member Constants
@@ -77,7 +77,7 @@ public:
     enum components { XA, XB, XC, XD, YA, YB, YC, YD, ZA, ZB, ZC, ZD };
 
 
-    // Generated Methods
+    // Generated Methods: copy construct/assignment
 
         //- Default construct
         BarycentricTensor() = default;
@@ -97,6 +97,7 @@ public:
         );
 
         //- Construct given four vector components (columns)
+        //  Eg, the corners of a tetrahedron
         inline BarycentricTensor
         (
             const Vector<Cmpt>& a,
@@ -108,18 +109,44 @@ public:
 
     // Member Functions
 
-        // Row-barycentric access
+    // Component access
 
-            inline Barycentric<Cmpt> x() const;
-            inline Barycentric<Cmpt> y() const;
-            inline Barycentric<Cmpt> z() const;
+        inline const Cmpt& xa() const;
+        inline const Cmpt& xb() const;
+        inline const Cmpt& xc() const;
+        inline const Cmpt& xd() const;
 
-        // Column-vector access
+        inline const Cmpt& ya() const;
+        inline const Cmpt& yb() const;
+        inline const Cmpt& yc() const;
+        inline const Cmpt& yd() const;
 
-            inline Vector<Cmpt> a() const;
-            inline Vector<Cmpt> b() const;
-            inline Vector<Cmpt> c() const;
-            inline Vector<Cmpt> d() const;
+        inline const Cmpt& za() const;
+        inline const Cmpt& zb() const;
+        inline const Cmpt& zc() const;
+        inline const Cmpt& zd() const;
+
+
+    // Row-barycentric access
+
+        inline Barycentric<Cmpt> x() const;
+        inline Barycentric<Cmpt> y() const;
+        inline Barycentric<Cmpt> z() const;
+
+
+    // Column-vector access
+
+        inline Vector<Cmpt> a() const;
+        inline Vector<Cmpt> b() const;
+        inline Vector<Cmpt> c() const;
+        inline Vector<Cmpt> d() const;
+
+
+    // Operations
+
+        //- Tensor/barycentric inner product
+        //  (transforms barycentric coordinates to vector)
+        inline Vector<Cmpt> inner(const Barycentric<Cmpt>& bry) const;
 };
 
 
diff --git a/src/OpenFOAM/primitives/Barycentric/BarycentricTensorI.H b/src/OpenFOAM/primitives/Barycentric/BarycentricTensorI.H
index 5c591733d6..1c73e89f6c 100644
--- a/src/OpenFOAM/primitives/Barycentric/BarycentricTensorI.H
+++ b/src/OpenFOAM/primitives/Barycentric/BarycentricTensorI.H
@@ -6,6 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2017 OpenFOAM Foundation
+    Copyright (C) 2022 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -87,6 +88,90 @@ inline Foam::BarycentricTensor<Cmpt>::BarycentricTensor
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
+template<class Cmpt>
+inline const Cmpt& Foam::BarycentricTensor<Cmpt>::xa() const
+{
+    return this->v_[XA];
+}
+
+
+template<class Cmpt>
+inline const Cmpt& Foam::BarycentricTensor<Cmpt>::xb() const
+{
+    return this->v_[XB];
+}
+
+
+template<class Cmpt>
+inline const Cmpt& Foam::BarycentricTensor<Cmpt>::xc() const
+{
+    return this->v_[XC];
+}
+
+
+template<class Cmpt>
+inline const Cmpt& Foam::BarycentricTensor<Cmpt>::xd() const
+{
+    return this->v_[XD];
+}
+
+
+template<class Cmpt>
+inline const Cmpt& Foam::BarycentricTensor<Cmpt>::ya() const
+{
+    return this->v_[YA];
+}
+
+
+template<class Cmpt>
+inline const Cmpt& Foam::BarycentricTensor<Cmpt>::yb() const
+{
+    return this->v_[YB];
+}
+
+
+template<class Cmpt>
+inline const Cmpt& Foam::BarycentricTensor<Cmpt>::yc() const
+{
+    return this->v_[YC];
+}
+
+
+template<class Cmpt>
+inline const Cmpt& Foam::BarycentricTensor<Cmpt>::yd() const
+{
+    return this->v_[YD];
+}
+
+
+template<class Cmpt>
+inline const Cmpt& Foam::BarycentricTensor<Cmpt>::za() const
+{
+    return this->v_[ZA];
+}
+
+
+template<class Cmpt>
+inline const Cmpt& Foam::BarycentricTensor<Cmpt>::zb() const
+{
+    return this->v_[ZB];
+}
+
+
+template<class Cmpt>
+inline const Cmpt& Foam::BarycentricTensor<Cmpt>::zc() const
+{
+    return this->v_[ZC];
+}
+
+
+template<class Cmpt>
+inline const Cmpt& Foam::BarycentricTensor<Cmpt>::zd() const
+{
+    return this->v_[ZD];
+}
+
+
 template<class Cmpt>
 inline Foam::Barycentric<Cmpt> Foam::BarycentricTensor<Cmpt>::x() const
 {
@@ -157,6 +242,26 @@ inline Foam::Vector<Cmpt> Foam::BarycentricTensor<Cmpt>::d() const
 }
 
 
+// NB: same workaround for gcc (11+) failure on (tensor dot vector)
+// - not sure it will indeed be required here as well.
+template<class Cmpt>
+#if defined(__GNUC__) && !defined(__clang__)
+__attribute__((optimize("no-tree-vectorize")))
+#endif
+inline Foam::Vector<Cmpt>
+Foam::BarycentricTensor<Cmpt>::inner(const Barycentric<Cmpt>& bry) const
+{
+    const BarycentricTensor<Cmpt>& t = *this;
+
+    return Vector<Cmpt>
+    (
+        (bry.a()*t.xa() + bry.b()*t.xb() + bry.c()*t.xc() + bry.d()*t.xd()),
+        (bry.a()*t.ya() + bry.b()*t.yb() + bry.c()*t.yc() + bry.d()*t.yd()),
+        (bry.a()*t.za() + bry.b()*t.zb() + bry.c()*t.zc() + bry.d()*t.zd())
+    );
+}
+
+
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
 namespace Foam
@@ -164,17 +269,20 @@ namespace Foam
 
 // * * * * * * * * * * * * * * * Global Operators  * * * * * * * * * * * * * //
 
+// Transform Barycentric coordinates to Vector
 template<class Cmpt>
 inline Vector<Cmpt> operator&
 (
-    const BarycentricTensor<Cmpt>& T,
+    const BarycentricTensor<Cmpt>& t,
     const Barycentric<Cmpt>& b
 )
 {
-    return Vector<Cmpt>(T.x() & b, T.y() & b, T.z() & b);
+    return t.inner(b);
 }
 
 
+// Transform Vector to Barycentric coordinates.
+// Caution: the tensor must be inverse one (see particle.C)
 template<class Cmpt>
 inline Barycentric<Cmpt> operator&
 (
diff --git a/src/OpenFOAM/primitives/Barycentric2D/Barycentric2D.H b/src/OpenFOAM/primitives/Barycentric2D/Barycentric2D.H
index 729789853d..71a9712a68 100644
--- a/src/OpenFOAM/primitives/Barycentric2D/Barycentric2D.H
+++ b/src/OpenFOAM/primitives/Barycentric2D/Barycentric2D.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2017 OpenFOAM Foundation
-    Copyright (C) 2019-2020 OpenCFD Ltd.
+    Copyright (C) 2019-2022 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -36,8 +36,8 @@ SourceFiles
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef Barycentric2D_H
-#define Barycentric2D_H
+#ifndef Foam_Barycentric2D_H
+#define Foam_Barycentric2D_H
 
 #include "contiguous.H"
 #include "VectorSpace.H"
@@ -86,33 +86,31 @@ public:
         inline Barycentric2D(const Foam::zero);
 
         //- Construct from components
-        inline Barycentric2D
-        (
-            const Cmpt& va,
-            const Cmpt& vb,
-            const Cmpt& vc
-        );
+        inline Barycentric2D(const Cmpt& va, const Cmpt& vb, const Cmpt& vc);
+
+        //- Construct from two components, calculating third component
+        inline Barycentric2D(const Cmpt& va, const Cmpt& vb);
 
 
     // Member Functions
 
-    // Access
+    // Component access
 
         inline const Cmpt& a() const;
         inline const Cmpt& b() const;
         inline const Cmpt& c() const;
 
-
-    // Edit
-
         inline Cmpt& a();
         inline Cmpt& b();
         inline Cmpt& c();
 
 
-    // Tests
+    // Operations, Tests
 
-        //- True if any coordinates are negative
+        //- Scalar-product of \c this with another Barycentric2D.
+        inline Cmpt inner(const Barycentric2D<Cmpt>& b2) const;
+
+        //- True if any coordinate is negative
         inline bool outside() const;
 };
 
diff --git a/src/OpenFOAM/primitives/Barycentric2D/Barycentric2DI.H b/src/OpenFOAM/primitives/Barycentric2D/Barycentric2DI.H
index a015b33bfa..ab9ec995b0 100644
--- a/src/OpenFOAM/primitives/Barycentric2D/Barycentric2DI.H
+++ b/src/OpenFOAM/primitives/Barycentric2D/Barycentric2DI.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2017 OpenFOAM Foundation
-    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2022 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -49,6 +49,17 @@ inline Foam::Barycentric2D<Cmpt>::Barycentric2D
 }
 
 
+template<class Cmpt>
+inline Foam::Barycentric2D<Cmpt>::Barycentric2D
+(
+    const Cmpt& va,
+    const Cmpt& vb
+)
+:
+    Barycentric2D<Cmpt>(va, vb, (pTraits<Cmpt>::one - va - vb))
+{}
+
+
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
 template<class Cmpt>
@@ -93,6 +104,20 @@ inline Cmpt& Foam::Barycentric2D<Cmpt>::c()
 }
 
 
+// * * * * * * * * * * * * * * * Member Operations * * * * * * * * * * * * * //
+
+template<class Cmpt>
+inline Cmpt Foam::Barycentric2D<Cmpt>::inner
+(
+    const Barycentric2D<Cmpt>& b2
+) const
+{
+    const Barycentric2D<Cmpt>& b1 = *this;
+
+    return (b1.a()*b2.a() + b1.b()*b2.b() + b1.c()*b2.c());
+}
+
+
 template<class Cmpt>
 inline bool Foam::Barycentric2D<Cmpt>::outside() const
 {
@@ -114,7 +139,7 @@ inline Cmpt operator&
     const Barycentric2D<Cmpt>& b2
 )
 {
-    return b1.a()*b2.a() + b1.b()*b2.b() + b1.c()*b2.c();
+    return b1.inner(b2);
 }
 
 
diff --git a/src/OpenFOAM/primitives/Tensor/TensorI.H b/src/OpenFOAM/primitives/Tensor/TensorI.H
index e6662fbde9..a9fc78d440 100644
--- a/src/OpenFOAM/primitives/Tensor/TensorI.H
+++ b/src/OpenFOAM/primitives/Tensor/TensorI.H
@@ -1069,7 +1069,7 @@ template<class Cmpt>
 // Workaround for gcc (11+) that fails to handle tensor dot vector
 __attribute__((optimize("no-tree-vectorize")))
 #endif
-inline typename innerProduct<Tensor<Cmpt>, Vector<Cmpt>>::type
+inline Vector<Cmpt>
 operator&(const Tensor<Cmpt>& t, const Vector<Cmpt>& v)
 {
     return Vector<Cmpt>
@@ -1083,7 +1083,7 @@ operator&(const Tensor<Cmpt>& t, const Vector<Cmpt>& v)
 
 //- Inner-product of a Vector and a Tensor
 template<class Cmpt>
-inline typename innerProduct<Vector<Cmpt>, Tensor<Cmpt>>::type
+inline Vector<Cmpt>
 operator&(const Vector<Cmpt>& v, const Tensor<Cmpt>& t)
 {
     return Vector<Cmpt>
diff --git a/src/OpenFOAM/primitives/Vector/Vector.H b/src/OpenFOAM/primitives/Vector/Vector.H
index 05ae0934c1..fff9290a98 100644
--- a/src/OpenFOAM/primitives/Vector/Vector.H
+++ b/src/OpenFOAM/primitives/Vector/Vector.H
@@ -30,7 +30,7 @@ Class
 Description
     Templated 3D Vector derived from VectorSpace adding construction from
     3 components, element access using x(), y() and z() member functions and
-    the inner-product (dot-product) and cross product operators.
+    the inner-product (dot-product) and cross-product operators.
 
     A centre() member function which returns the Vector for which it is called
     is defined so that point which is a typedef to Vector\<scalar\> behaves as
@@ -130,6 +130,15 @@ public:
         //- Access to the vector z component
         inline Cmpt& z();
 
+
+    // Vector Operations
+
+        //- Return \c this (for point which is a typedef to Vector\<scalar\>)
+        inline const Vector<Cmpt>& centre
+        (
+            const Foam::UList<Vector<Cmpt>>&  /* (unused) */
+        ) const noexcept;
+
         //- Inplace normalise the vector by its magnitude
         //  For small magnitudes (less than ROOTVSMALL) set to zero.
         //  Will not be particularly useful for a vector of labels
@@ -139,12 +148,11 @@ public:
         //- unit vector.
         inline Vector<Cmpt>& removeCollinear(const Vector<Cmpt>& unitVec);
 
+        //- Scalar-product of \c this with another Vector.
+        inline Cmpt inner(const Vector<Cmpt>& v2) const;
 
-        //- Return *this (used for point which is a typedef to Vector<scalar>.
-        inline const Vector<Cmpt>& centre
-        (
-            const Foam::UList<Vector<Cmpt>>&  /* (unused) */
-        ) const;
+        //- Cross-product of \c this with another Vector.
+        inline Vector<Cmpt> cross(const Vector<Cmpt>& v2) const;
 };
 
 
diff --git a/src/OpenFOAM/primitives/Vector/VectorI.H b/src/OpenFOAM/primitives/Vector/VectorI.H
index 3f697e1844..53373b2713 100644
--- a/src/OpenFOAM/primitives/Vector/VectorI.H
+++ b/src/OpenFOAM/primitives/Vector/VectorI.H
@@ -113,7 +113,7 @@ template<class Cmpt>
 inline const Foam::Vector<Cmpt>& Foam::Vector<Cmpt>::centre
 (
     const Foam::UList<Vector<Cmpt>>&
-) const
+) const noexcept
 {
     return *this;
 }
@@ -146,6 +146,32 @@ Foam::Vector<Cmpt>::removeCollinear(const Vector<Cmpt>& unitVec)
 }
 
 
+// * * * * * * * * * * * * * * * Member Operations * * * * * * * * * * * * * //
+
+template<class Cmpt>
+inline Cmpt Foam::Vector<Cmpt>::inner(const Vector<Cmpt>& v2) const
+{
+    const Vector<Cmpt>& v1 = *this;
+
+    return (v1.x()*v2.x() + v1.y()*v2.y() + v1.z()*v2.z());
+}
+
+
+template<class Cmpt>
+inline Foam::Vector<Cmpt>
+Foam::Vector<Cmpt>::cross(const Vector<Cmpt>& v2) const
+{
+    const Vector<Cmpt>& v1 = *this;
+
+    return Vector<Cmpt>
+    (
+        (v1.y()*v2.z() - v1.z()*v2.y()),
+        (v1.z()*v2.x() - v1.x()*v2.z()),
+        (v1.x()*v2.y() - v1.y()*v2.x())
+    );
+}
+
+
 // * * * * * * * * * * * * * * * Global Operators  * * * * * * * * * * * * * //
 
 namespace Foam
@@ -153,8 +179,9 @@ namespace Foam
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
-//- Dummy innerProduct for scalar to allow the construction of vtables for
-//  virtual member functions involving the inner-products of fields
+//- Dummy innerProduct for scalar
+//  Allows the construction of vtables for virtual member functions
+//  involving the inner-products of fields
 //  for which a "NotImplemented" specialization for scalar is provided.
 template<class Cmpt>
 class innerProduct<Vector<Cmpt>, scalar>
@@ -166,22 +193,16 @@ public:
 
 
 template<class Cmpt>
-inline typename innerProduct<Vector<Cmpt>, Vector<Cmpt>>::type
-operator&(const Vector<Cmpt>& v1, const Vector<Cmpt>& v2)
+inline Cmpt operator&(const Vector<Cmpt>& v1, const Vector<Cmpt>& v2)
 {
-    return Cmpt(v1.x()*v2.x() + v1.y()*v2.y() + v1.z()*v2.z());
+    return v1.inner(v2);
 }
 
 
 template<class Cmpt>
 inline Vector<Cmpt> operator^(const Vector<Cmpt>& v1, const Vector<Cmpt>& v2)
 {
-    return Vector<Cmpt>
-    (
-        (v1.y()*v2.z() - v1.z()*v2.y()),
-        (v1.z()*v2.x() - v1.x()*v2.z()),
-        (v1.x()*v2.y() - v1.y()*v2.x())
-    );
+    return v1.cross(v2);
 }
 
 
diff --git a/src/OpenFOAM/primitives/Vector2D/Vector2DI.H b/src/OpenFOAM/primitives/Vector2D/Vector2DI.H
index a5c63b818d..3095c39ef4 100644
--- a/src/OpenFOAM/primitives/Vector2D/Vector2DI.H
+++ b/src/OpenFOAM/primitives/Vector2D/Vector2DI.H
@@ -125,8 +125,7 @@ namespace Foam
 // * * * * * * * * * * * * * * * Global Operators  * * * * * * * * * * * * * //
 
 template<class Cmpt>
-inline typename innerProduct<Vector2D<Cmpt>, Vector2D<Cmpt>>::type
-operator&(const Vector2D<Cmpt>& v1, const Vector2D<Cmpt>& v2)
+inline Cmpt operator&(const Vector2D<Cmpt>& v1, const Vector2D<Cmpt>& v2)
 {
     return Cmpt(v1.x()*v2.x() + v1.y()*v2.y());
 }
diff --git a/src/OpenFOAM/primitives/VectorSpace/VectorSpace.H b/src/OpenFOAM/primitives/VectorSpace/VectorSpace.H
index 11ef9ffb51..814769e795 100644
--- a/src/OpenFOAM/primitives/VectorSpace/VectorSpace.H
+++ b/src/OpenFOAM/primitives/VectorSpace/VectorSpace.H
@@ -39,8 +39,8 @@ SourceFiles
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef VectorSpace_H
-#define VectorSpace_H
+#ifndef Foam_VectorSpace_H
+#define Foam_VectorSpace_H
 
 #include "direction.H"
 #include "scalar.H"
diff --git a/src/dynamicMesh/motionSmoother/polyMeshGeometry/polyMeshGeometry.C b/src/dynamicMesh/motionSmoother/polyMeshGeometry/polyMeshGeometry.C
index 59a2cce429..89e717596a 100644
--- a/src/dynamicMesh/motionSmoother/polyMeshGeometry/polyMeshGeometry.C
+++ b/src/dynamicMesh/motionSmoother/polyMeshGeometry/polyMeshGeometry.C
@@ -28,8 +28,8 @@ License
 
 #include "polyMeshGeometry.H"
 #include "polyMeshTetDecomposition.H"
-#include "pyramidPointFaceRef.H"
-#include "tetPointRef.H"
+#include "pyramid.H"
+#include "tetrahedron.H"
 #include "syncTools.H"
 #include "unitConversion.H"
 #include "primitiveMeshTools.H"
diff --git a/src/dynamicMesh/polyTopoChange/polyTopoChange/tetDecomposer.C b/src/dynamicMesh/polyTopoChange/polyTopoChange/tetDecomposer.C
index f86c4446c7..963f32fc4e 100644
--- a/src/dynamicMesh/polyTopoChange/polyTopoChange/tetDecomposer.C
+++ b/src/dynamicMesh/polyTopoChange/polyTopoChange/tetDecomposer.C
@@ -34,7 +34,7 @@ License
 #include "OFstream.H"
 #include "edgeHashes.H"
 #include "syncTools.H"
-#include "triPointRef.H"
+#include "triangle.H"
 
 // * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
 
diff --git a/src/dynamicMesh/slidingInterface/coupleSlidingInterface.C b/src/dynamicMesh/slidingInterface/coupleSlidingInterface.C
index e8e814e321..e478f846cd 100644
--- a/src/dynamicMesh/slidingInterface/coupleSlidingInterface.C
+++ b/src/dynamicMesh/slidingInterface/coupleSlidingInterface.C
@@ -33,7 +33,7 @@ License
 #include "enrichedPatch.H"
 #include "DynamicList.H"
 #include "pointHit.H"
-#include "triPointRef.H"
+#include "triangle.H"
 #include "plane.H"
 #include "polyTopoChanger.H"
 #include "polyAddPoint.H"
diff --git a/src/fileFormats/obj/OBJstream.H b/src/fileFormats/obj/OBJstream.H
index 2b319aedf3..b30800fe5b 100644
--- a/src/fileFormats/obj/OBJstream.H
+++ b/src/fileFormats/obj/OBJstream.H
@@ -35,14 +35,14 @@ SourceFiles
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef OBJstream_H
-#define OBJstream_H
+#ifndef Foam_OBJstream_H
+#define Foam_OBJstream_H
 
 #include "OFstream.H"
 #include "point.H"
 #include "edge.H"
 #include "face.H"
-#include "triPointRef.H"
+#include "triangle.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
diff --git a/src/fileFormats/stl/STLtriangle.H b/src/fileFormats/stl/STLtriangle.H
index c8e49a23c9..0072db268a 100644
--- a/src/fileFormats/stl/STLtriangle.H
+++ b/src/fileFormats/stl/STLtriangle.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
-    Copyright (C) 2016-2017 OpenCFD Ltd.
+    Copyright (C) 2016-2022 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -35,9 +35,10 @@ SourceFiles
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef STLtriangle_H
-#define STLtriangle_H
+#ifndef Foam_STLtriangle_H
+#define Foam_STLtriangle_H
 
+#include <cstdint>
 #include "STLpoint.H"
 #include "Istream.H"
 #include "Ostream.H"
@@ -60,7 +61,7 @@ class STLtriangle
     // Typedefs
 
     //- Attribute is 16-bit
-    typedef unsigned short STLattrib;
+    typedef uint16_t STLattrib;
 
     // Private data
     // NB: The order of the members (1 normal, 3 points, 1 attribute) is
@@ -78,8 +79,8 @@ public:
 
     // Constructors
 
-        //- Construct null
-        inline STLtriangle();
+        //- Default construct
+        STLtriangle() = default;
 
         //- Construct from components
         inline STLtriangle
@@ -88,7 +89,7 @@ public:
             const STLpoint& a,
             const STLpoint& b,
             const STLpoint& c,
-            unsigned short attrib
+            uint16_t attrib
         );
 
         //- Construct from istream (read binary)
@@ -99,11 +100,11 @@ public:
 
         // Access
 
-            inline const STLpoint& normal() const;
-            inline const STLpoint& a() const;
-            inline const STLpoint& b() const;
-            inline const STLpoint& c() const;
-            inline unsigned short attrib() const;
+            const STLpoint& normal() const noexcept { return normal_; }
+            const STLpoint& a() const noexcept { return a_; }
+            const STLpoint& b() const noexcept { return b_; }
+            const STLpoint& c() const noexcept { return c_; }
+            uint16_t attrib() const noexcept { return attrib_; }
 
 
         // Read
diff --git a/src/fileFormats/stl/STLtriangleI.H b/src/fileFormats/stl/STLtriangleI.H
index b53f2df7be..8348c9546d 100644
--- a/src/fileFormats/stl/STLtriangleI.H
+++ b/src/fileFormats/stl/STLtriangleI.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011 OpenFOAM Foundation
-    Copyright (C) 2016 OpenCFD Ltd.
+    Copyright (C) 2016-2022 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -26,21 +26,17 @@ License
 
 \*---------------------------------------------------------------------------*/
 
-#include "triPointRef.H"
+#include "triangle.H"
 
 // * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
-inline Foam::STLtriangle::STLtriangle()
-{}
-
-
 inline Foam::STLtriangle::STLtriangle
 (
     const STLpoint& normal,
     const STLpoint& a,
     const STLpoint& b,
     const STLpoint& c,
-    unsigned short attrib
+    uint16_t attrib
 )
 :
     normal_(normal),
@@ -59,36 +55,6 @@ inline Foam::STLtriangle::STLtriangle(std::istream& is)
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
-inline const Foam::STLpoint& Foam::STLtriangle::normal() const
-{
-    return normal_;
-}
-
-
-inline const Foam::STLpoint& Foam::STLtriangle::a() const
-{
-    return a_;
-}
-
-
-inline const Foam::STLpoint& Foam::STLtriangle::b() const
-{
-    return b_;
-}
-
-
-inline const Foam::STLpoint& Foam::STLtriangle::c() const
-{
-    return c_;
-}
-
-
-inline unsigned short Foam::STLtriangle::attrib() const
-{
-    return attrib_;
-}
-
-
 inline void Foam::STLtriangle::read(std::istream& is)
 {
     is.read(reinterpret_cast<char*>(&normal_), 4*sizeof(STLpoint));
diff --git a/src/fileFormats/vtk/read/vtkUnstructuredReader.C b/src/fileFormats/vtk/read/vtkUnstructuredReader.C
index 60d47b512a..52e6ca8cc2 100644
--- a/src/fileFormats/vtk/read/vtkUnstructuredReader.C
+++ b/src/fileFormats/vtk/read/vtkUnstructuredReader.C
@@ -32,7 +32,7 @@ License
 #include "stringIOList.H"
 #include "cellModel.H"
 #include "vectorIOField.H"
-#include "triPointRef.H"
+#include "triangle.H"
 #include "stringOps.H"
 
 /* * * * * * * * * * * * * * * Static Member Data  * * * * * * * * * * * * * */
diff --git a/src/finiteArea/faMesh/faMeshDemandDrivenData.C b/src/finiteArea/faMesh/faMeshDemandDrivenData.C
index 397732b70e..c5df1546b9 100644
--- a/src/finiteArea/faMesh/faMeshDemandDrivenData.C
+++ b/src/finiteArea/faMesh/faMeshDemandDrivenData.C
@@ -37,7 +37,7 @@ License
 #include "processorFaPatchFields.H"
 #include "emptyFaPatchFields.H"
 #include "wedgeFaPatch.H"
-#include "triPointRef.H"
+#include "triangle.H"
 
 // * * * * * * * * * * * * * * * Local Functions * * * * * * * * * * * * * * //
 
diff --git a/src/lagrangian/DSMC/submodels/InflowBoundaryModel/FreeStream/FreeStream.C b/src/lagrangian/DSMC/submodels/InflowBoundaryModel/FreeStream/FreeStream.C
index 1123e12cb2..21e6d47839 100644
--- a/src/lagrangian/DSMC/submodels/InflowBoundaryModel/FreeStream/FreeStream.C
+++ b/src/lagrangian/DSMC/submodels/InflowBoundaryModel/FreeStream/FreeStream.C
@@ -27,7 +27,6 @@ License
 
 #include "FreeStream.H"
 #include "constants.H"
-#include "triPointRef.H"
 #include "tetIndices.H"
 
 using namespace Foam::constant::mathematical;
diff --git a/src/lagrangian/basic/particle/particle.H b/src/lagrangian/basic/particle/particle.H
index 135cecf30b..dfe9dd15aa 100644
--- a/src/lagrangian/basic/particle/particle.H
+++ b/src/lagrangian/basic/particle/particle.H
@@ -32,8 +32,8 @@ Description
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef particle_H
-#define particle_H
+#ifndef Foam_particle_H
+#define Foam_particle_H
 
 #include "vector.H"
 #include "barycentric.H"
@@ -43,7 +43,6 @@ Description
 #include "pointField.H"
 #include "faceList.H"
 #include "OFstream.H"
-#include "tetPointRef.H"
 #include "FixedList.H"
 #include "polyMeshTetDecomposition.H"
 #include "particleMacros.H"
diff --git a/src/lagrangian/intermediate/submodels/Kinematic/InjectionModel/PatchInjection/patchInjectionBase.C b/src/lagrangian/intermediate/submodels/Kinematic/InjectionModel/PatchInjection/patchInjectionBase.C
index 7f8e012bf6..2f5043d418 100644
--- a/src/lagrangian/intermediate/submodels/Kinematic/InjectionModel/PatchInjection/patchInjectionBase.C
+++ b/src/lagrangian/intermediate/submodels/Kinematic/InjectionModel/PatchInjection/patchInjectionBase.C
@@ -29,7 +29,7 @@ License
 #include "polyMesh.H"
 #include "SubField.H"
 #include "Random.H"
-#include "triPointRef.H"
+#include "triangle.H"
 #include "volFields.H"
 #include "polyMeshTetDecomposition.H"
 
diff --git a/src/mesh/snappyHexMesh/snappyHexMeshDriver/snappySnapDriverFeature.C b/src/mesh/snappyHexMesh/snappyHexMeshDriver/snappySnapDriverFeature.C
index dbed336572..1cef7db8cd 100644
--- a/src/mesh/snappyHexMesh/snappyHexMeshDriver/snappySnapDriverFeature.C
+++ b/src/mesh/snappyHexMesh/snappyHexMeshDriver/snappySnapDriverFeature.C
@@ -41,7 +41,7 @@ License
 #include "indexedOctree.H"
 #include "snapParameters.H"
 #include "PatchTools.H"
-#include "pyramidPointFaceRef.H"
+#include "pyramid.H"
 #include "localPointRegion.H"
 
 // * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
diff --git a/src/meshTools/AMIInterpolation/AMIInterpolation/AMIInterpolation.C b/src/meshTools/AMIInterpolation/AMIInterpolation/AMIInterpolation.C
index 382ddfa653..d03d360c4c 100644
--- a/src/meshTools/AMIInterpolation/AMIInterpolation/AMIInterpolation.C
+++ b/src/meshTools/AMIInterpolation/AMIInterpolation/AMIInterpolation.C
@@ -31,7 +31,7 @@ License
 #include "mapDistribute.H"
 #include "flipOp.H"
 #include "profiling.H"
-#include "triPointRef.H"
+#include "triangle.H"
 #include "OFstream.H"
 
 // * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
diff --git a/src/meshTools/AMIInterpolation/faceAreaIntersect/faceAreaIntersect.H b/src/meshTools/AMIInterpolation/faceAreaIntersect/faceAreaIntersect.H
index d79327de31..fc2d559021 100644
--- a/src/meshTools/AMIInterpolation/faceAreaIntersect/faceAreaIntersect.H
+++ b/src/meshTools/AMIInterpolation/faceAreaIntersect/faceAreaIntersect.H
@@ -44,7 +44,7 @@ SourceFiles
 #include "FixedList.H"
 #include "plane.H"
 #include "face.H"
-#include "triPoints.H"
+#include "triangle.H"
 #include "Enum.H"
 #include "searchableSurface.H"
 
diff --git a/src/meshTools/indexedOctree/treeDataEdge.H b/src/meshTools/indexedOctree/treeDataEdge.H
index f501c2a73f..04cbe30612 100644
--- a/src/meshTools/indexedOctree/treeDataEdge.H
+++ b/src/meshTools/indexedOctree/treeDataEdge.H
@@ -35,11 +35,11 @@ SourceFiles
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef treeDataEdge_H
-#define treeDataEdge_H
+#ifndef Foam_treeDataEdge_H
+#define Foam_treeDataEdge_H
 
 #include "treeBoundBoxList.H"
-#include "linePointRef.H"
+#include "line.H"
 #include "volumeType.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
@@ -47,7 +47,7 @@ SourceFiles
 namespace Foam
 {
 
-// Forward declaration of classes
+// Forward Declarations
 template<class Type> class indexedOctree;
 
 /*---------------------------------------------------------------------------*\
diff --git a/src/meshTools/indexedOctree/treeDataPoint.H b/src/meshTools/indexedOctree/treeDataPoint.H
index eb10107da0..e368cc84fa 100644
--- a/src/meshTools/indexedOctree/treeDataPoint.H
+++ b/src/meshTools/indexedOctree/treeDataPoint.H
@@ -40,12 +40,12 @@ SourceFiles
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef treeDataPoint_H
-#define treeDataPoint_H
+#ifndef Foam_treeDataPoint_H
+#define Foam_treeDataPoint_H
 
 #include "pointField.H"
 #include "treeBoundBox.H"
-#include "linePointRef.H"
+#include "line.H"
 #include "volumeType.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
@@ -53,7 +53,7 @@ SourceFiles
 namespace Foam
 {
 
-// Forward declarations
+// Forward Declarations
 template<class Type> class indexedOctree;
 
 /*---------------------------------------------------------------------------*\
diff --git a/src/meshTools/mappedPatches/mappedPolyPatch/mappedPatchBase.C b/src/meshTools/mappedPatches/mappedPolyPatch/mappedPatchBase.C
index 89ec09d907..29a590e6e5 100644
--- a/src/meshTools/mappedPatches/mappedPolyPatch/mappedPatchBase.C
+++ b/src/meshTools/mappedPatches/mappedPolyPatch/mappedPatchBase.C
@@ -42,7 +42,7 @@ License
 #include "Time.H"
 #include "mapDistribute.H"
 #include "SubField.H"
-#include "triPointRef.H"
+#include "triangle.H"
 #include "syncTools.H"
 #include "treeDataCell.H"
 #include "DynamicField.H"
diff --git a/src/meshTools/primitiveMeshGeometry/primitiveMeshGeometry.C b/src/meshTools/primitiveMeshGeometry/primitiveMeshGeometry.C
index e05fa1ed92..a7b0a89113 100644
--- a/src/meshTools/primitiveMeshGeometry/primitiveMeshGeometry.C
+++ b/src/meshTools/primitiveMeshGeometry/primitiveMeshGeometry.C
@@ -27,9 +27,9 @@ License
 \*---------------------------------------------------------------------------*/
 
 #include "primitiveMeshGeometry.H"
-#include "pyramidPointFaceRef.H"
+#include "pyramid.H"
 #include "unitConversion.H"
-#include "triPointRef.H"
+#include "triangle.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
diff --git a/src/meshTools/searchableSurfaces/searchableSurface/searchableSurface.H b/src/meshTools/searchableSurfaces/searchableSurface/searchableSurface.H
index 38d0052668..a05928b605 100644
--- a/src/meshTools/searchableSurfaces/searchableSurface/searchableSurface.H
+++ b/src/meshTools/searchableSurfaces/searchableSurface/searchableSurface.H
@@ -41,15 +41,15 @@ SourceFiles
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef searchableSurface_H
-#define searchableSurface_H
+#ifndef Foam_searchableSurface_H
+#define Foam_searchableSurface_H
 
 #include "pointField.H"
 #include "boundBox.H"
 #include "typeInfo.H"
 #include "runTimeSelectionTables.H"
 #include "pointIndexHit.H"
-#include "linePointRef.H"
+#include "line.H"
 #include "objectRegistry.H"
 #include "volumeType.H"
 
@@ -58,7 +58,7 @@ SourceFiles
 namespace Foam
 {
 
-// Forward declarations
+// Forward Declarations
 class objectRegistry;
 class mapDistribute;
 class treeBoundBox;
diff --git a/src/meshTools/tetOverlapVolume/tetOverlapVolume.C b/src/meshTools/tetOverlapVolume/tetOverlapVolume.C
index c65c1a73cf..d8cadb99bf 100644
--- a/src/meshTools/tetOverlapVolume/tetOverlapVolume.C
+++ b/src/meshTools/tetOverlapVolume/tetOverlapVolume.C
@@ -28,7 +28,6 @@ License
 
 #include "tetOverlapVolume.H"
 #include "tetrahedron.H"
-#include "tetPoints.H"
 #include "polyMesh.H"
 #include "OFstream.H"
 #include "treeBoundBox.H"
@@ -43,12 +42,6 @@ namespace Foam
 }
 
 
-// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
-
-Foam::tetOverlapVolume::tetOverlapVolume()
-{}
-
-
 // * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * * * //
 
 Foam::treeBoundBox Foam::tetOverlapVolume::pyrBb
diff --git a/src/meshTools/tetOverlapVolume/tetOverlapVolume.H b/src/meshTools/tetOverlapVolume/tetOverlapVolume.H
index 5fd8abff2f..39f281323d 100644
--- a/src/meshTools/tetOverlapVolume/tetOverlapVolume.H
+++ b/src/meshTools/tetOverlapVolume/tetOverlapVolume.H
@@ -35,8 +35,8 @@ SourceFiles
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef tetOverlapVolume_H
-#define tetOverlapVolume_H
+#ifndef Foam_tetOverlapVolume_H
+#define Foam_tetOverlapVolume_H
 
 #include "FixedList.H"
 #include "labelList.H"
@@ -47,6 +47,7 @@ SourceFiles
 namespace Foam
 {
 
+// Forward Declarations
 class primitiveMesh;
 class polyMesh;
 
@@ -56,7 +57,7 @@ class polyMesh;
 
 class tetOverlapVolume
 {
-    // Private classes
+    // Private Classes
 
         //- tetPoints handling : sum resulting volumes
         class sumMomentOp
@@ -184,14 +185,14 @@ public:
 
     // Constructors
 
-        //- Null constructor
-        tetOverlapVolume();
+        //- Default construct
+        tetOverlapVolume() = default;
 
 
     // Public members
 
         //- Return a list of cells in meshA which overlaps with cellBI in
-        // meshB
+        //- meshB
         labelList overlappingCells
         (
             const polyMesh& meshA,
diff --git a/src/meshTools/triSurface/surfaceFeatures/surfaceFeatures.C b/src/meshTools/triSurface/surfaceFeatures/surfaceFeatures.C
index 422c78e4be..81deec2603 100644
--- a/src/meshTools/triSurface/surfaceFeatures/surfaceFeatures.C
+++ b/src/meshTools/triSurface/surfaceFeatures/surfaceFeatures.C
@@ -32,7 +32,6 @@ License
 #include "treeDataEdge.H"
 #include "treeDataPoint.H"
 #include "meshTools.H"
-#include "linePointRef.H"
 #include "Fstream.H"
 #include "unitConversion.H"
 #include "edgeHashes.H"
diff --git a/src/meshTools/triSurface/surfaceLocation/surfaceLocation.H b/src/meshTools/triSurface/surfaceLocation/surfaceLocation.H
index 8e97cff8d4..6516da4fa0 100644
--- a/src/meshTools/triSurface/surfaceLocation/surfaceLocation.H
+++ b/src/meshTools/triSurface/surfaceLocation/surfaceLocation.H
@@ -49,7 +49,7 @@ SourceFiles
 #define surfaceLocation_H
 
 #include "pointIndexHit.H"
-#include "triPointRef.H"
+#include "triangle.H"
 #include "InfoProxy.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
diff --git a/src/meshTools/triSurface/triSurfaceTools/triSurfaceTools.H b/src/meshTools/triSurface/triSurfaceTools/triSurfaceTools.H
index aa0adee18a..891304d4ff 100644
--- a/src/meshTools/triSurface/triSurfaceTools/triSurfaceTools.H
+++ b/src/meshTools/triSurface/triSurfaceTools/triSurfaceTools.H
@@ -61,7 +61,7 @@ SourceFiles
 #include "FixedList.H"
 #include "Pair.H"
 #include "vector2D.H"
-#include "triPointRef.H"
+#include "triangle.H"
 #include "surfaceLocation.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
@@ -69,7 +69,7 @@ SourceFiles
 namespace Foam
 {
 
-// Forward declaration of classes
+// Forward Declarations
 class boundBox;
 class edge;
 class labelledTri;
diff --git a/src/meshTools/triSurface/triangleFuncs/triangleFuncs.C b/src/meshTools/triSurface/triangleFuncs/triangleFuncs.C
index dc2ad74b03..39328ddab5 100644
--- a/src/meshTools/triSurface/triangleFuncs/triangleFuncs.C
+++ b/src/meshTools/triSurface/triangleFuncs/triangleFuncs.C
@@ -27,11 +27,11 @@ License
 \*---------------------------------------------------------------------------*/
 
 #include "triangleFuncs.H"
+#include "triangle.H"
 #include "pointField.H"
 #include "treeBoundBox.H"
 #include "SortableList.H"
 #include "boolList.H"
-#include "triPointRef.H"
 
 // * * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * //
 
diff --git a/src/meshTools/triSurface/triangleFuncs/triangleFuncs.H b/src/meshTools/triSurface/triangleFuncs/triangleFuncs.H
index 8d3068d33a..1c4c5cdde5 100644
--- a/src/meshTools/triSurface/triangleFuncs/triangleFuncs.H
+++ b/src/meshTools/triSurface/triangleFuncs/triangleFuncs.H
@@ -35,8 +35,8 @@ SourceFiles
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef triangleFuncs_H
-#define triangleFuncs_H
+#ifndef Foam_triangleFuncs_H
+#define Foam_triangleFuncs_H
 
 #include "pointField.H"
 
diff --git a/src/sampling/surface/isoSurface/isoSurfaceCell.C b/src/sampling/surface/isoSurface/isoSurfaceCell.C
index 5c94e349ae..26176aa379 100644
--- a/src/sampling/surface/isoSurface/isoSurfaceCell.C
+++ b/src/sampling/surface/isoSurface/isoSurfaceCell.C
@@ -36,7 +36,7 @@ License
 #include "triSurface.H"
 #include "triSurfaceTools.H"
 #include "Time.H"
-#include "triPoints.H"
+#include "triangle.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
diff --git a/src/sampling/surface/isoSurface/isoSurfacePoint.C b/src/sampling/surface/isoSurface/isoSurfacePoint.C
index 21b34190b9..b4be87d417 100644
--- a/src/sampling/surface/isoSurface/isoSurfacePoint.C
+++ b/src/sampling/surface/isoSurface/isoSurfacePoint.C
@@ -32,7 +32,7 @@ License
 #include "volFields.H"
 #include "triSurfaceTools.H"
 #include "triSurface.H"
-#include "triPoints.H"
+#include "triangle.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
diff --git a/src/sampling/surface/isoSurface/isoSurfaceTopo.C b/src/sampling/surface/isoSurface/isoSurfaceTopo.C
index 92c15e1fc5..3267ff8934 100644
--- a/src/sampling/surface/isoSurface/isoSurfaceTopo.C
+++ b/src/sampling/surface/isoSurface/isoSurfaceTopo.C
@@ -31,7 +31,6 @@ License
 #include "volFields.H"
 #include "edgeHashes.H"
 #include "tetCell.H"
-#include "tetPointRef.H"
 #include "DynamicField.H"
 #include "syncTools.H"
 #include "indirectPrimitivePatch.H"
diff --git a/src/surfMesh/surfaceFormats/stl/STLsurfaceFormat.C b/src/surfMesh/surfaceFormats/stl/STLsurfaceFormat.C
index 6bc87cd8ae..b5df5d43be 100644
--- a/src/surfMesh/surfaceFormats/stl/STLsurfaceFormat.C
+++ b/src/surfMesh/surfaceFormats/stl/STLsurfaceFormat.C
@@ -27,7 +27,7 @@ License
 \*---------------------------------------------------------------------------*/
 
 #include "STLsurfaceFormat.H"
-#include "triPointRef.H"
+#include "triangle.H"
 #include "ListOps.H"
 
 // * * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * //