diff --git a/applications/utilities/surface/surfaceCheck/surfaceCheck.C b/applications/utilities/surface/surfaceCheck/surfaceCheck.C
index 577f1470ae..a5e8429cb9 100644
--- a/applications/utilities/surface/surfaceCheck/surfaceCheck.C
+++ b/applications/utilities/surface/surfaceCheck/surfaceCheck.C
@@ -47,19 +47,16 @@ bool validTri
 
     const labelledTri& f = surf[faceI];
 
-    if
-    (
-        (f[0] < 0) || (f[0] >= surf.points().size())
-     || (f[1] < 0) || (f[1] >= surf.points().size())
-     || (f[2] < 0) || (f[2] >= surf.points().size())
-    )
+    forAll(f, fp)
     {
-        WarningIn("validTri(const triSurface&, const label)")
-            << "triangle " << faceI << " vertices " << f
-            << " uses point indices outside point range 0.."
-            << surf.points().size()-1 << endl;
-
-        return false;
+        if (f[fp] < 0 || f[fp] >= surf.points().size())
+        {
+            WarningIn("validTri(const triSurface&, const label)")
+                << "triangle " << faceI << " vertices " << f
+                << " uses point indices outside point range 0.."
+                << surf.points().size()-1 << endl;
+            return false;
+        }
     }
 
     if ((f[0] == f[1]) || (f[0] == f[2]) || (f[1] == f[2]))
diff --git a/applications/utilities/surface/surfaceClean/collapseBase.C b/applications/utilities/surface/surfaceClean/collapseBase.C
index dd92967a5f..109aa07248 100644
--- a/applications/utilities/surface/surfaceClean/collapseBase.C
+++ b/applications/utilities/surface/surfaceClean/collapseBase.C
@@ -100,8 +100,8 @@ static void splitTri
     label oldNTris = tris.size();
 
     label fp = findIndex(f, e[0]);
-    label fp1 = (fp+1)%3;
-    label fp2 = (fp1+1)%3;
+    label fp1 = f.fcIndex(fp);
+    label fp2 = f.fcIndex(fp1);
 
     if (f[fp1] == e[1])
     {
diff --git a/applications/utilities/surface/surfaceClean/collapseEdge.C b/applications/utilities/surface/surfaceClean/collapseEdge.C
index 66fba4cd97..c7be020cab 100644
--- a/applications/utilities/surface/surfaceClean/collapseEdge.C
+++ b/applications/utilities/surface/surfaceClean/collapseEdge.C
@@ -34,7 +34,7 @@ static void markPointNbrs
     boolList& okToCollapse
 )
 {
-    const labelledTri& f = surf.localFaces()[faceI];
+    const triSurface::FaceType& f = surf.localFaces()[faceI];
 
     forAll(f, fp)
     {
@@ -108,12 +108,12 @@ label collapseEdge(triSurface& surf, const scalar minLen)
             if (okToCollapse[faceI])
             {
                 // Check edge lengths.
-                const labelledTri& f = localFaces[faceI];
+                const triSurface::FaceType& f = localFaces[faceI];
 
                 forAll(f, fp)
                 {
                     label v = f[fp];
-                    label v1 = f[(fp+1) % 3];
+                    label v1 = f[f.fcIndex(fp)];
 
                     if (mag(localPoints[v1] - localPoints[v]) < minLen)
                     {
diff --git a/applications/utilities/surface/surfaceSplitNonManifolds/surfaceSplitNonManifolds.C b/applications/utilities/surface/surfaceSplitNonManifolds/surfaceSplitNonManifolds.C
index e52a32010a..2611a7863a 100644
--- a/applications/utilities/surface/surfaceSplitNonManifolds/surfaceSplitNonManifolds.C
+++ b/applications/utilities/surface/surfaceSplitNonManifolds/surfaceSplitNonManifolds.C
@@ -128,9 +128,7 @@ void dumpFaces
 
     forAllConstIter(Map<label>, connectedFaces, iter)
     {
-        const labelledTri& f = surf.localFaces()[iter.key()];
-
-        point ctr(f.centre(surf.localPoints()));
+        point ctr = surf.localFaces()[iter.key()].centre(surf.localPoints());
 
         os  << "v " << ctr.x() << ' ' << ctr.y() << ' ' << ctr.z() << endl;
     }
@@ -453,7 +451,7 @@ label sharedFace
 
     const edge& e = surf.edges()[sharedEdgeI];
 
-    const labelledTri& f = surf.localFaces()[firstFaceI];
+    const triSurface::FaceType& f = surf.localFaces()[firstFaceI];
 
     label startIndex = findIndex(f, e.start());
 
@@ -597,13 +595,13 @@ void renumberFaces
     const triSurface& surf,
     const labelList& pointMap,
     const Map<label>& faceToEdge,
-    List<labelledTri>& newTris
+    List<triSurface::FaceType>& newTris
 )
 {
     forAllConstIter(Map<label>, faceToEdge, iter)
     {
         const label faceI = iter.key();
-        const labelledTri& f = surf.localFaces()[faceI];
+        const triSurface::FaceType& f = surf.localFaces()[faceI];
 
         forAll(f, fp)
         {
@@ -911,7 +909,6 @@ int main(int argc, char *argv[])
         forAll(surf, faceI)
         {
             newTris[faceI] = surf.localFaces()[faceI];
-
             newTris[faceI].region() = surf[faceI].region();
         }
 
@@ -924,7 +921,7 @@ int main(int argc, char *argv[])
         // Check if faces use unmoved points.
         forAll(newTris, faceI)
         {
-            const labelledTri& f = newTris[faceI];
+            const triSurface::FaceType& f = newTris[faceI];
 
             forAll(f, fp)
             {
diff --git a/applications/utilities/surface/surfaceSubset/surfaceSubset.C b/applications/utilities/surface/surfaceSubset/surfaceSubset.C
index 6bc54d40ad..cdd718c320 100644
--- a/applications/utilities/surface/surfaceSubset/surfaceSubset.C
+++ b/applications/utilities/surface/surfaceSubset/surfaceSubset.C
@@ -196,8 +196,7 @@ int main(int argc, char *argv[])
 
         forAll(surf1, faceI)
         {
-            const labelledTri& f = surf1[faceI];
-            const point centre = f.centre(surf1.points());
+            const point centre = surf1[faceI].centre(surf1.points());
 
             if
             (
diff --git a/src/meshTools/indexedOctree/treeDataTriSurface.C b/src/meshTools/indexedOctree/treeDataTriSurface.C
index 81cad2948b..1bae779e5e 100644
--- a/src/meshTools/indexedOctree/treeDataTriSurface.C
+++ b/src/meshTools/indexedOctree/treeDataTriSurface.C
@@ -324,13 +324,7 @@ void Foam::treeDataTriSurface::findNearest
     forAll(indices, i)
     {
         label index = indices[i];
-        const labelledTri& f = surface_[index];
-
-        // Triangle points
-        const point& p0 = points[f[0]];
-        const point& p1 = points[f[1]];
-        const point& p2 = points[f[2]];
-
+        const triSurface::FaceType& f = surface_[index];
 
         ////- Possible optimization: do quick rejection of triangle if bounding
         ////  sphere does not intersect triangle bounding box. From simplistic
@@ -379,7 +373,7 @@ void Foam::treeDataTriSurface::findNearest
             //     t
             // );
 
-            pointHit pHit = triPointRef(p0, p1, p2).nearestPoint(sample);
+            pointHit pHit = f.nearestPoint(sample, points);
 
             scalar distSqr = sqr(pHit.distance());
 
@@ -425,14 +419,16 @@ bool Foam::treeDataTriSurface::intersects
 {
     const pointField& points = surface_.points();
 
-    const labelledTri& f = surface_[index];
+    const triSurface::FaceType& f = surface_[index];
 
     // Do quick rejection test
     treeBoundBox triBb(points[f[0]], points[f[0]]);
-    triBb.min() = min(triBb.min(), points[f[1]]);
-    triBb.max() = max(triBb.max(), points[f[1]]);
-    triBb.min() = min(triBb.min(), points[f[2]]);
-    triBb.max() = max(triBb.max(), points[f[2]]);
+
+    for (label ptI=1; ptI < f.size(); ++ptI)
+    {
+        triBb.min() = ::Foam::min(triBb.min(), points[f[ptI]]);
+        triBb.max() = ::Foam::max(triBb.max(), points[f[ptI]]);
+    }
 
     const direction startBits(triBb.posBits(start));
     const direction endBits(triBb.posBits(end));
@@ -443,16 +439,14 @@ bool Foam::treeDataTriSurface::intersects
         return false;
     }
 
-    const triPointRef tri(points[f[0]], points[f[1]], points[f[2]]);
-
     const vector dir(end - start);
 
     // Use relative tolerance (from octree) to determine intersection.
-
-    pointHit inter = tri.intersection
+    pointHit inter = f.intersection
     (
         start,
         dir,
+        points,
         intersection::HALF_RAY,
         indexedOctree<treeDataTriSurface>::perturbTol()
     );
diff --git a/src/meshTools/searchableSurface/triSurfaceMesh.C b/src/meshTools/searchableSurface/triSurfaceMesh.C
index bc01d8d40e..058c26a0d4 100644
--- a/src/meshTools/searchableSurface/triSurfaceMesh.C
+++ b/src/meshTools/searchableSurface/triSurfaceMesh.C
@@ -162,7 +162,7 @@ bool Foam::triSurfaceMesh::isSurfaceClosed() const
         facesPerEdge.clear();
         forAll(pFaces, i)
         {
-            const labelledTri& f = triSurface::operator[](pFaces[i]);
+            const triSurface::FaceType& f = triSurface::operator[](pFaces[i]);
             label fp = findIndex(f, pointI);
 
             // Something weird: if I expand the code of addFaceToEdge in both
@@ -293,9 +293,9 @@ void Foam::triSurfaceMesh::calcBounds(boundBox& bb, label& nPoints) const
     nPoints = 0;
     bb = boundBox::invertedBox;
 
-    forAll(s, triI)
+    forAll(s, faceI)
     {
-        const labelledTri& f = s[triI];
+        const triSurface::FaceType& f = s[faceI];
 
         forAll(f, fp)
         {
@@ -475,9 +475,9 @@ void Foam::triSurfaceMesh::clearOut()
 Foam::pointField Foam::triSurfaceMesh::coordinates() const
 {
     // Use copy to calculate face centres so they don't get stored
-    return PrimitivePatch<labelledTri, SubList, const pointField&>
+    return PrimitivePatch<triSurface::FaceType, SubList, const pointField&>
     (
-        SubList<labelledTri>(*this, triSurface::size()),
+        SubList<triSurface::FaceType>(*this, triSurface::size()),
         triSurface::points()
     ).faceCentres();
 }
@@ -804,12 +804,12 @@ void Foam::triSurfaceMesh::getNormal
     {
         if (info[i].hit())
         {
-            label triI = info[i].index();
+            label faceI = info[i].index();
             //- Cached:
-            //normal[i] = faceNormals()[triI];
+            //normal[i] = faceNormals()[faceI];
 
             //- Uncached
-            normal[i] = triSurface::operator[](triI).normal(points());
+            normal[i] = triSurface::operator[](faceI).normal(points());
             normal[i] /= mag(normal[i]) + VSMALL;
         }
         else
diff --git a/src/meshTools/triSurface/booleanOps/booleanSurface/booleanSurface.C b/src/meshTools/triSurface/booleanOps/booleanSurface/booleanSurface.C
index dc0da28405..115149ebd3 100644
--- a/src/meshTools/triSurface/booleanOps/booleanSurface/booleanSurface.C
+++ b/src/meshTools/triSurface/booleanOps/booleanSurface/booleanSurface.C
@@ -489,7 +489,7 @@ Foam::booleanSurface::booleanSurface
     }
 
     labelList faceZone1;
-    (void)cutSurf1.markZones(isIntersectionEdge1, faceZone1);
+    cutSurf1.markZones(isIntersectionEdge1, faceZone1);
 
 
     // Check whether at least one of sides of intersection has been marked.
@@ -537,7 +537,7 @@ Foam::booleanSurface::booleanSurface
     }
 
     labelList faceZone2;
-    (void)cutSurf2.markZones(isIntersectionEdge2, faceZone2);
+    cutSurf2.markZones(isIntersectionEdge2, faceZone2);
 
 
     // Check whether at least one of sides of intersection has been marked.
@@ -960,20 +960,11 @@ Foam::booleanSurface::booleanSurface
 
     forAll(combinedSurf, faceI)
     {
-        const labelledTri& f = combinedSurf[faceI];
-
-        pointHit curHit =
-            triPointRef
-            (
-                pts[f[0]],
-                pts[f[1]],
-                pts[f[2]]
-            ).nearestPoint(outsidePoint);
+        pointHit curHit = combinedSurf[faceI].nearestPoint(outsidePoint, pts);
 
         if (curHit.distance() < minHit.distance())
         {
             minHit = curHit;
-
             minFaceI = faceI;
         }
     }
diff --git a/src/meshTools/triSurface/booleanOps/intersectedSurface/intersectedSurface.C b/src/meshTools/triSurface/booleanOps/intersectedSurface/intersectedSurface.C
index 672b9efe6c..592c15bd62 100644
--- a/src/meshTools/triSurface/booleanOps/intersectedSurface/intersectedSurface.C
+++ b/src/meshTools/triSurface/booleanOps/intersectedSurface/intersectedSurface.C
@@ -219,12 +219,12 @@ bool Foam::intersectedSurface::sameEdgeOrder
         if (fpB != -1)
         {
             // Get prev/next vertex on fA
-            label vA1 = fA[(fpA + 1) % 3];
-            label vAMin1 = fA[fpA ? fpA-1 : 2];
+            label vA1 = fA[fA.fcIndex(fpA)];
+            label vAMin1 = fA[fA.rcIndex(fpA)];
 
             // Get prev/next vertex on fB
-            label vB1 = fB[(fpB + 1) % 3];
-            label vBMin1 = fB[fpB ? fpB-1 : 2];
+            label vB1 = fB[fB.fcIndex(fpB)];
+            label vBMin1 = fB[fB.rcIndex(fpB)];
 
             if (vA1 == vB1 || vAMin1 == vBMin1)
             {
diff --git a/src/meshTools/triSurface/booleanOps/surfaceIntersection/edgeIntersections.C b/src/meshTools/triSurface/booleanOps/surfaceIntersection/edgeIntersections.C
index c8955f7470..12974a0436 100644
--- a/src/meshTools/triSurface/booleanOps/surfaceIntersection/edgeIntersections.C
+++ b/src/meshTools/triSurface/booleanOps/surfaceIntersection/edgeIntersections.C
@@ -414,23 +414,14 @@ bool Foam::edgeIntersections::offsetPerturb
         // Classify point on face of surface2
         label surf2FaceI = pHit.index();
 
-        const labelledTri& f2 = surf2.localFaces()[surf2FaceI];
-
+        const triSurface::FaceType& f2 = surf2.localFaces()[surf2FaceI];
         const pointField& surf2Pts = surf2.localPoints();
 
-        label nearType;
-        label nearLabel;
+        const point ctr = f2.centre(surf2Pts);
 
-        triPointRef tri
-        (
-            surf2Pts[f2[0]],
-            surf2Pts[f2[1]],
-            surf2Pts[f2[2]]
-        );
+        label nearType, nearLabel;
 
-        point ctr = tri.centre();
-
-        tri.classify(pHit.hitPoint(), nearType, nearLabel);
+        f2.nearestPointClassify(pHit.hitPoint(), surf2Pts, nearType, nearLabel);
 
         if (nearType == triPointRef::POINT || nearType == triPointRef::EDGE)
         {
diff --git a/src/meshTools/triSurface/booleanOps/surfaceIntersection/surfaceIntersection.C b/src/meshTools/triSurface/booleanOps/surfaceIntersection/surfaceIntersection.C
index 58c206aa75..561b73d084 100644
--- a/src/meshTools/triSurface/booleanOps/surfaceIntersection/surfaceIntersection.C
+++ b/src/meshTools/triSurface/booleanOps/surfaceIntersection/surfaceIntersection.C
@@ -53,22 +53,18 @@ bool Foam::surfaceIntersection::excludeEdgeHit
     const scalar
 )
 {
-    const labelledTri& f = surf.localFaces()[faceI];
-
+    const triSurface::FaceType& f = surf.localFaces()[faceI];
     const edge& e = surf.edges()[edgeI];
 
-    if
-    (
-        (f[0] == e.start())
-     || (f[0] == e.end())
-     || (f[1] == e.start())
-     || (f[1] == e.end())
-     || (f[2] == e.start())
-     || (f[2] == e.end())
-    )
+    forAll(f, fp)
     {
-        return true;
+        if (f[0] == e.start() || f[0] == e.end())
+        {
+            return true;
+        }
+    }
 
+// {
 //        // Get edge vector
 //        vector eVec = e.vec(surf.localPoints());
 //        eVec /= mag(eVec) + VSMALL;
@@ -112,11 +108,9 @@ bool Foam::surfaceIntersection::excludeEdgeHit
 //        {
 //            return false;
 //        }
-    }
-    else
-    {
-        return false;
-    }
+// }
+
+    return false;
 }
 
 
@@ -137,14 +131,14 @@ bool Foam::surfaceIntersection::excludeEdgeHit
 //
 //    const pointField& points = surf.points();
 //
-//    const labelledTri& f = surf.localFaces()[hitFaceI];
+//    const triSurface::FaceType& f = surf.localFaces()[hitFaceI];
 //
 //    // Plane for intersect test.
 //    plane pl(eStart, n);
 //
 //    forAll(f, fp)
 //    {
-//        label fp1 = (fp + 1) % 3;
+//        label fp1 = f.fcIndex(fp);
 //
 //        const point& start = points[f[fp]];
 //        const point& end = points[f[fp1]];
@@ -303,19 +297,12 @@ void Foam::surfaceIntersection::classifyHit
 
     // Classify point on surface2
 
-    const labelledTri& f2 = surf2.localFaces()[surf2FaceI];
-
+    const triSurface::FaceType& f2 = surf2.localFaces()[surf2FaceI];
     const pointField& surf2Pts = surf2.localPoints();
 
-    label nearType;
-    label nearLabel;
+    label nearType, nearLabel;
 
-    (void)triPointRef
-    (
-        surf2Pts[f2[0]],
-        surf2Pts[f2[1]],
-        surf2Pts[f2[2]]
-    ).classify(pHit.hitPoint(), nearType, nearLabel);
+    f2.nearestPointClassify(pHit.hitPoint(), surf2Pts, nearType, nearLabel);
 
     // Classify points on edge of surface1
     label edgeEnd =
@@ -333,7 +320,7 @@ void Foam::surfaceIntersection::classifyHit
         if (edgeEnd >= 0)
         {
             // 1. Point hits point. Do nothing.
-            if (debug&2)
+            if (debug & 2)
             {
                 Pout<< pHit.hitPoint() << " is surf1:"
                     << " end point of edge " << e
@@ -344,7 +331,7 @@ void Foam::surfaceIntersection::classifyHit
         else
         {
             // 2. Edge hits point. Cut edge with new point.
-            if (debug&2)
+            if (debug & 2)
             {
                 Pout<< pHit.hitPoint() << " is surf1:"
                     << " somewhere on edge " << e
diff --git a/src/meshTools/triSurface/booleanOps/surfaceIntersection/surfaceIntersectionFuncs.C b/src/meshTools/triSurface/booleanOps/surfaceIntersection/surfaceIntersectionFuncs.C
index 18ebd6988c..eb0868ff3f 100644
--- a/src/meshTools/triSurface/booleanOps/surfaceIntersection/surfaceIntersectionFuncs.C
+++ b/src/meshTools/triSurface/booleanOps/surfaceIntersection/surfaceIntersectionFuncs.C
@@ -90,9 +90,7 @@ Foam::label Foam::surfaceIntersection::getEdge
     const label fp
 )
 {
-    const labelledTri& f = surf.localFaces()[faceI];
-
-    edge faceEdge(f[fp], f[(fp+1) % 3]);
+    const edge faceEdge = surf.localFaces()[faceI].faceEdge(fp);
 
     const labelList& eLabels = surf.faceEdges()[faceI];
 
diff --git a/src/meshTools/triSurface/octreeData/octreeDataTriSurface.C b/src/meshTools/triSurface/octreeData/octreeDataTriSurface.C
index 55e60a3111..7f78f4c2a0 100644
--- a/src/meshTools/triSurface/octreeData/octreeDataTriSurface.C
+++ b/src/meshTools/triSurface/octreeData/octreeDataTriSurface.C
@@ -340,15 +340,7 @@ Foam::label Foam::octreeDataTriSurface::getSampleType
             << abort(FatalError);
     }
 
-    const pointField& pts = surface_.points();
-    const labelledTri& f = surface_[faceI];
-
-    pointHit curHit = triPointRef
-    (
-        pts[f[0]],
-        pts[f[1]],
-        pts[f[2]]
-    ).nearestPoint(sample);
+    pointHit curHit = surface_[faceI].nearestPoint(sample, surface_.points());
 
     // Get normal according to position on face. On point -> pointNormal,
     // on edge-> edge normal, face normal on interior.
@@ -433,18 +425,18 @@ bool Foam::octreeDataTriSurface::intersects
         return false;
     }
 
-    const pointField& points = surface_.points();
-
-    const labelledTri& f = surface_[index];
-
-    triPointRef tri(points[f[0]], points[f[1]], points[f[2]]);
-
     const vector dir(end - start);
 
     // Disable picking up intersections behind us.
     scalar oldTol = intersection::setPlanarTol(0.0);
 
-    pointHit inter = tri.ray(start, dir, intersection::HALF_RAY);
+    pointHit inter = surface_[index].ray
+    (
+        start,
+        dir,
+        surface_.points(),
+        intersection::HALF_RAY
+    );
 
     intersection::setPlanarTol(oldTol);
 
@@ -512,10 +504,8 @@ Foam::scalar Foam::octreeDataTriSurface::calcSign
 {
     n = surface_.faceNormals()[index];
 
-    const labelledTri& tri = surface_[index];
-
-    // take vector from sample to any point on triangle (we use vertex 0)
-    vector vec = sample - surface_.points()[tri[0]];
+    // take vector from sample to any point on face (we use vertex 0)
+    vector vec = sample - surface_.points()[surface_[index][0]];
 
     vec /= mag(vec) + VSMALL;
 
diff --git a/src/meshTools/triSurface/orientedSurface/orientedSurface.C b/src/meshTools/triSurface/orientedSurface/orientedSurface.C
index 38a7afd4b8..9c78bb1053 100644
--- a/src/meshTools/triSurface/orientedSurface/orientedSurface.C
+++ b/src/meshTools/triSurface/orientedSurface/orientedSurface.C
@@ -34,38 +34,15 @@ defineTypeNameAndDebug(Foam::orientedSurface, 0);
 
 // * * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * //
 
-// Return true if face uses edge from start to end.
-bool Foam::orientedSurface::edgeOrder
-(
-    const labelledTri& f,
-    const edge& e
-)
-{
-    if
-    (
-        (f[0] == e[0] && f[1] == e[1])
-     || (f[1] == e[0] && f[2] == e[1])
-     || (f[2] == e[0] && f[0] == e[1])
-    )
-    {
-        return true;
-    }
-    else
-    {
-        return false;
-    }
-}
-
-
 // Return true if edge is used in opposite order in faces
 bool Foam::orientedSurface::consistentEdge
 (
     const edge& e,
-    const labelledTri& f0,
-    const labelledTri& f1
+    const triSurface::FaceType& f0,
+    const triSurface::FaceType& f1
 )
 {
-    return edgeOrder(f0, e) ^ edgeOrder(f1, e);
+    return (f0.edgeDirection(e) > 0) ^ (f1.edgeDirection(e) > 0);
 }
 
 
@@ -118,8 +95,8 @@ Foam::labelList Foam::orientedSurface::edgeToFace
             label face0 = eFaces[0];
             label face1 = eFaces[1];
 
-            const labelledTri& f0 = s.localFaces()[face0];
-            const labelledTri& f1 = s.localFaces()[face1];
+            const triSurface::FaceType& f0 = s.localFaces()[face0];
+            const triSurface::FaceType& f1 = s.localFaces()[face1];
 
             if (flip[face0] == UNVISITED)
             {
@@ -401,15 +378,8 @@ bool Foam::orientedSurface::orient
         {
             if (flipState[faceI] == UNVISITED)
             {
-                const labelledTri& f = s[faceI];
-
                 pointHit curHit =
-                    triPointRef
-                    (
-                        s.points()[f[0]],
-                        s.points()[f[1]],
-                        s.points()[f[2]]
-                    ).nearestPoint(samplePoint);
+                    s[faceI].nearestPoint(samplePoint, s.points());
 
                 if (curHit.distance() < minDist)
                 {
diff --git a/src/meshTools/triSurface/orientedSurface/orientedSurface.H b/src/meshTools/triSurface/orientedSurface/orientedSurface.H
index c4f15e0dc6..8bfa3106cf 100644
--- a/src/meshTools/triSurface/orientedSurface/orientedSurface.H
+++ b/src/meshTools/triSurface/orientedSurface/orientedSurface.H
@@ -66,15 +66,12 @@ class orientedSurface
 
     // Private Member Functions
 
-        //- Return true if face uses edge from start to end.
-        static bool edgeOrder(const labelledTri&, const edge&);
-
         //- Return true if edge is used in opposite order in faces
         static bool consistentEdge
         (
             const edge& e,
-            const labelledTri& f0,
-            const labelledTri& f1
+            const triSurface::FaceType& f0,
+            const triSurface::FaceType& f1
         );
 
         //- From changed faces get the changed edges
diff --git a/src/meshTools/triSurface/triSurfaceTools/triSurfaceTools.C b/src/meshTools/triSurface/triSurfaceTools/triSurfaceTools.C
index af30b3bcc8..ba0161219e 100644
--- a/src/meshTools/triSurface/triSurfaceTools/triSurfaceTools.C
+++ b/src/meshTools/triSurface/triSurfaceTools/triSurfaceTools.C
@@ -1111,7 +1111,7 @@ void Foam::triSurfaceTools::snapToEnd
         if (current.elementType() == triPointRef::NONE)
         {
             // endpoint on point; current on triangle
-            const labelledTri& f = s.localFaces()[current.index()];
+            const triSurface::FaceType& f = s.localFaces()[current.index()];
 
             if (findIndex(f, end.index()) != -1)
             {
@@ -1566,8 +1566,7 @@ Foam::label Foam::triSurfaceTools::oppositeVertex
     const label edgeI
 )
 {
-    const labelledTri& f = surf.localFaces()[faceI];
-
+    const triSurface::FaceType& f = surf.localFaces()[faceI];
     const edge& e = surf.edges()[edgeI];
 
     forAll(f, fp)
@@ -1601,7 +1600,6 @@ Foam::label Foam::triSurfaceTools::getEdge
     forAll(v1Edges, v1EdgeI)
     {
         label edgeI = v1Edges[v1EdgeI];
-
         const edge& e = surf.edges()[edgeI];
 
         if ((e.start() == v2) || (e.end() == v2))
@@ -2116,18 +2114,12 @@ Foam::vector Foam::triSurfaceTools::surfaceNormal
     const point& nearestPt
 )
 {
-    const labelledTri& f = surf[nearestFaceI];
+    const triSurface::FaceType& f = surf[nearestFaceI];
     const pointField& points = surf.points();
 
-    label nearType;
-    label nearLabel;
+    label nearType, nearLabel;
 
-    triPointRef
-    (
-        points[f[0]],
-        points[f[1]],
-        points[f[2]]
-    ).classify(nearestPt, nearType, nearLabel);
+    f.nearestPointClassify(nearestPt, points, nearType, nearLabel);
 
     if (nearType == triPointRef::NONE)
     {
@@ -2153,7 +2145,7 @@ Foam::vector Foam::triSurfaceTools::surfaceNormal
     else
     {
         // Nearest to point
-        const labelledTri& localF = surf.localFaces()[nearestFaceI];
+        const triSurface::FaceType& localF = surf.localFaces()[nearestFaceI];
         return surf.pointNormals()[localF[nearLabel]];
     }
 }
@@ -2203,18 +2195,13 @@ Foam::triSurfaceTools::sideType Foam::triSurfaceTools::surfaceSide
     const label nearestFaceI
 )
 {
-    const labelledTri& f = surf[nearestFaceI];
+    const triSurface::FaceType& f = surf[nearestFaceI];
     const pointField& points = surf.points();
 
-    // Find where point is on triangle.
+    // Find where point is on face
     label nearType, nearLabel;
 
-    pointHit pHit = triPointRef
-    (
-        points[f[0]],
-        points[f[1]],
-        points[f[2]]
-    ).nearestPointClassify(sample, nearType, nearLabel);
+    pointHit pHit = f.nearestPointClassify(sample, points, nearType, nearLabel);
 
     const point& nearestPoint(pHit.rawPoint());
 
@@ -2304,7 +2291,7 @@ Foam::triSurfaceTools::sideType Foam::triSurfaceTools::surfaceSide
         // above (nearType == triPointRef::EDGE).
 
 
-        const labelledTri& localF = surf.localFaces()[nearestFaceI];
+        const triSurface::FaceType& localF = surf.localFaces()[nearestFaceI];
         label nearPointI = localF[nearLabel];
 
         const edgeList& edges = surf.edges();
@@ -2497,7 +2484,7 @@ Foam::triSurface Foam::triSurfaceTools::triangulateFaceCentre
 
             forAll(f, fp)
             {
-                label fp1 = (fp + 1) % f.size();
+                label fp1 = f.fcIndex(fp);
 
                 triangles.append(labelledTri(f[fp], f[fp1], fc, newPatchI));
 
diff --git a/src/parallel/distributed/distributedTriSurfaceMesh/distributedTriSurfaceMesh.C b/src/parallel/distributed/distributedTriSurfaceMesh/distributedTriSurfaceMesh.C
index accee92b3f..dab87130cc 100644
--- a/src/parallel/distributed/distributedTriSurfaceMesh/distributedTriSurfaceMesh.C
+++ b/src/parallel/distributed/distributedTriSurfaceMesh/distributedTriSurfaceMesh.C
@@ -903,18 +903,13 @@ Foam::distributedTriSurfaceMesh::independentlyDistributedBbs
         point& bbMin = bbs[distribution[triI]][0].min();
         point& bbMax = bbs[distribution[triI]][0].max();
 
-        const labelledTri& f = s[triI];
-        const point& p0 = s.points()[f[0]];
-        const point& p1 = s.points()[f[1]];
-        const point& p2 = s.points()[f[2]];
-
-        bbMin = min(bbMin, p0);
-        bbMin = min(bbMin, p1);
-        bbMin = min(bbMin, p2);
-
-        bbMax = max(bbMax, p0);
-        bbMax = max(bbMax, p1);
-        bbMax = max(bbMax, p2);
+        const triSurface::FaceType& f = s[triI];
+        forAll(f, fp)
+        {
+            const point& pt = s.points()[f[fp]];
+            bbMin = ::Foam::min(bbMin, pt);
+            bbMax = ::Foam::max(bbMax, pt);
+        }
     }
 
     // Now combine for all processors and convert to correct format.
@@ -1003,12 +998,12 @@ void Foam::distributedTriSurfaceMesh::subsetMeshMap
                 // Store new faces compact
                 newToOldFaces[faceI++] = oldFacei;
 
-                // Renumber labels for triangle
-                const labelledTri& tri = s[oldFacei];
+                // Renumber labels for face
+                const triSurface::FaceType& f = s[oldFacei];
 
-                forAll(tri, fp)
+                forAll(f, fp)
                 {
-                    label oldPointI = tri[fp];
+                    label oldPointI = f[fp];
 
                     if (oldToNewPoints[oldPointI] == -1)
                     {
@@ -1122,12 +1117,12 @@ Foam::triSurface Foam::distributedTriSurfaceMesh::subsetMesh
         {
             if (include[oldFacei])
             {
-                // Renumber labels for triangle
-                const labelledTri& tri = s[oldFacei];
+                // Renumber labels for face
+                const triSurface::FaceType& f = s[oldFacei];
 
-                forAll(tri, fp)
+                forAll(f, fp)
                 {
-                    label oldPointI = tri[fp];
+                    label oldPointI = f[fp];
 
                     if (oldToNewPoints[oldPointI] == -1)
                     {
diff --git a/src/sampling/sampledSurface/isoSurface/isoSurfaceCell.C b/src/sampling/sampledSurface/isoSurface/isoSurfaceCell.C
index 9ac2a1d0e0..4948b41de1 100644
--- a/src/sampling/sampledSurface/isoSurface/isoSurfaceCell.C
+++ b/src/sampling/sampledSurface/isoSurface/isoSurfaceCell.C
@@ -931,19 +931,17 @@ bool Foam::isoSurfaceCell::validTri(const triSurface& surf, const label faceI)
 
     const labelledTri& f = surf[faceI];
 
-    if
-    (
-        (f[0] < 0) || (f[0] >= surf.points().size())
-     || (f[1] < 0) || (f[1] >= surf.points().size())
-     || (f[2] < 0) || (f[2] >= surf.points().size())
-    )
+    forAll(f, fp)
     {
-        WarningIn("validTri(const triSurface&, const label)")
-            << "triangle " << faceI << " vertices " << f
-            << " uses point indices outside point range 0.."
-            << surf.points().size()-1 << endl;
+        if (f[fp] < 0 || f[fp] >= surf.points().size())
+        {
+            WarningIn("validTri(const triSurface&, const label)")
+                << "triangle " << faceI << " vertices " << f
+                << " uses point indices outside point range 0.."
+                << surf.points().size()-1 << endl;
 
-        return false;
+            return false;
+        }
     }
 
     if ((f[0] == f[1]) || (f[0] == f[2]) || (f[1] == f[2]))
@@ -1337,12 +1335,12 @@ Foam::triSurface Foam::isoSurfaceCell::subsetMesh
         {
             if (include[oldFacei])
             {
-                // Renumber labels for triangle
-                const labelledTri& tri = s[oldFacei];
+                // Renumber labels for face
+                const triSurface::FaceType& f = s[oldFacei];
 
-                forAll(tri, fp)
+                forAll(f, fp)
                 {
-                    label oldPointI = tri[fp];
+                    label oldPointI = f[fp];
 
                     if (oldToNewPoints[oldPointI] == -1)
                     {
diff --git a/src/sampling/sampledSurface/sampledTriSurfaceMesh/sampledTriSurfaceMesh.C b/src/sampling/sampledSurface/sampledTriSurfaceMesh/sampledTriSurfaceMesh.C
index e846221ce8..9a58dc41c2 100644
--- a/src/sampling/sampledSurface/sampledTriSurfaceMesh/sampledTriSurfaceMesh.C
+++ b/src/sampling/sampledSurface/sampledTriSurfaceMesh/sampledTriSurfaceMesh.C
@@ -239,15 +239,15 @@ bool Foam::sampledTriSurfaceMesh::update()
 
     {
         label newPointI = 0;
-        label newTriI = 0;
+        label newFaceI = 0;
 
-        forAll(s, triI)
+        forAll(s, faceI)
         {
-            if (include[triI])
+            if (include[faceI])
             {
-                faceMap[newTriI++] = triI;
+                faceMap[newFaceI++] = faceI;
 
-                const labelledTri& f = s[triI];
+                const triSurface::FaceType& f = s[faceI];
                 forAll(f, fp)
                 {
                     if (reversePointMap[f[fp]] == -1)
@@ -258,7 +258,7 @@ bool Foam::sampledTriSurfaceMesh::update()
                 }
             }
         }
-        faceMap.setSize(newTriI);
+        faceMap.setSize(newFaceI);
         pointMap.setSize(newPointI);
     }
 
diff --git a/src/triSurface/tools/labelledTri/labelledTri.H b/src/triSurface/tools/labelledTri/labelledTri.H
index d8d57394be..70d5fbfffd 100644
--- a/src/triSurface/tools/labelledTri/labelledTri.H
+++ b/src/triSurface/tools/labelledTri/labelledTri.H
@@ -62,6 +62,13 @@ public:
         //- Construct null
         inline labelledTri();
 
+        //- Construct from triFace and a region label
+        inline labelledTri
+        (
+            const triFace&,
+            const label region
+        );
+
         //- Construct from three point labels and a region label
         inline labelledTri
         (
diff --git a/src/triSurface/tools/labelledTri/labelledTriI.H b/src/triSurface/tools/labelledTri/labelledTriI.H
index 91a2347f32..91c1a92134 100644
--- a/src/triSurface/tools/labelledTri/labelledTriI.H
+++ b/src/triSurface/tools/labelledTri/labelledTriI.H
@@ -21,41 +21,43 @@ License
     You should have received a copy of the GNU General Public License
     along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
 
-Description
-
 \*---------------------------------------------------------------------------*/
 
 #include "IOstreams.H"
 
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-namespace Foam
-{
-
 // * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
-//- Construct null
-inline labelledTri::labelledTri()
+inline Foam::labelledTri::labelledTri()
 :
     region_(-1)
 {}
 
 
-//- Construct from components
-inline labelledTri::labelledTri
+inline Foam::labelledTri::labelledTri
 (
-    const label A,
-    const label B,
-    const label C,
+    const triFace& tri,
     const label region
 )
 :
-    triFace(A, B, C),
+    triFace(tri),
     region_(region)
 {}
 
 
-inline labelledTri::labelledTri(Istream& is)
+inline Foam::labelledTri::labelledTri
+(
+    const label a,
+    const label b,
+    const label c,
+    const label region
+)
+:
+    triFace(a, b, c),
+    region_(region)
+{}
+
+
+inline Foam::labelledTri::labelledTri(Istream& is)
 {
     operator>>(is, *this);
 }
@@ -63,12 +65,12 @@ inline labelledTri::labelledTri(Istream& is)
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
-inline label labelledTri::region() const
+inline Foam::label Foam::labelledTri::region() const
 {
     return region_;
 }
 
-inline label& labelledTri::region()
+inline Foam::label& Foam::labelledTri::region()
 {
     return region_;
 }
@@ -76,7 +78,7 @@ inline label& labelledTri::region()
 
 // * * * * * * * * * * * * * * * Ostream Operator  * * * * * * * * * * * * * //
 
-inline Istream& operator>>(Istream& is, labelledTri& t)
+inline Foam::Istream& Foam::operator>>(Istream& is, labelledTri& t)
 {
     if (is.format() == IOstream::ASCII)
     {
@@ -100,7 +102,7 @@ inline Istream& operator>>(Istream& is, labelledTri& t)
 }
 
 
-inline Ostream& operator<<(Ostream& os, const labelledTri& t)
+inline Foam::Ostream& Foam::operator<<(Ostream& os, const labelledTri& t)
 {
     if (os.format() == IOstream::ASCII)
     {
@@ -125,8 +127,4 @@ inline Ostream& operator<<(Ostream& os, const labelledTri& t)
 }
 
 
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-} // End namespace Foam
-
 // ************************************************************************* //
diff --git a/src/triSurface/triSurface/interfaces/AC3D/writeAC.C b/src/triSurface/triSurface/interfaces/AC3D/writeAC.C
index 8be7289526..53b3b37291 100644
--- a/src/triSurface/triSurface/interfaces/AC3D/writeAC.C
+++ b/src/triSurface/triSurface/interfaces/AC3D/writeAC.C
@@ -26,14 +26,10 @@ License
 #include "triSurface.H"
 #include "IOmanip.H"
 
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-namespace Foam
-{
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
-void triSurface::writeAC(Ostream& os) const
+void Foam::triSurface::writeAC(Ostream& os) const
 {
     // Write with patches as separate objects under "world" object.
     // Header is taken over from sample file.
@@ -140,8 +136,4 @@ void triSurface::writeAC(Ostream& os) const
 }
 
 
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-} // End namespace Foam
-
 // ************************************************************************* //
diff --git a/src/triSurface/triSurface/interfaces/GTS/readGTS.C b/src/triSurface/triSurface/interfaces/GTS/readGTS.C
index 2b45baa8eb..6ec57e3c39 100644
--- a/src/triSurface/triSurface/interfaces/GTS/readGTS.C
+++ b/src/triSurface/triSurface/interfaces/GTS/readGTS.C
@@ -27,14 +27,10 @@ License
 #include "IFstream.H"
 #include "IStringStream.H"
 
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-namespace Foam
-{
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
-bool triSurface::readGTS(const fileName& GTSfileName)
+bool Foam::triSurface::readGTS(const fileName& GTSfileName)
 {
     IFstream GTSfile(GTSfileName);
 
@@ -162,8 +158,4 @@ bool triSurface::readGTS(const fileName& GTSfileName)
 }
 
 
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-} // End namespace Foam
-
 // ************************************************************************* //
diff --git a/src/triSurface/triSurface/interfaces/OBJ/readOBJ.C b/src/triSurface/triSurface/interfaces/OBJ/readOBJ.C
index f2aa25aca7..8bfe966751 100644
--- a/src/triSurface/triSurface/interfaces/OBJ/readOBJ.C
+++ b/src/triSurface/triSurface/interfaces/OBJ/readOBJ.C
@@ -27,14 +27,9 @@ License
 #include "IFstream.H"
 #include "IStringStream.H"
 
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-namespace Foam
-{
-
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
-bool triSurface::readOBJ(const fileName& OBJfileName)
+bool Foam::triSurface::readOBJ(const fileName& OBJfileName)
 {
     IFstream OBJfile(OBJfileName);
 
@@ -195,8 +190,4 @@ bool triSurface::readOBJ(const fileName& OBJfileName)
 }
 
 
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-} // End namespace Foam
-
 // ************************************************************************* //
diff --git a/src/triSurface/triSurface/interfaces/OFF/readOFF.C b/src/triSurface/triSurface/interfaces/OFF/readOFF.C
index 66e995c46b..67a7cc45a0 100644
--- a/src/triSurface/triSurface/interfaces/OFF/readOFF.C
+++ b/src/triSurface/triSurface/interfaces/OFF/readOFF.C
@@ -30,14 +30,9 @@ Description
 #include "IFstream.H"
 #include "IStringStream.H"
 
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-namespace Foam
-{
-
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
-bool triSurface::readOFF(const fileName& OFFfileName)
+bool Foam::triSurface::readOFF(const fileName& OFFfileName)
 {
     IFstream OFFfile(OFFfileName);
 
@@ -136,8 +131,4 @@ bool triSurface::readOFF(const fileName& OFFfileName)
 }
 
 
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-} // End namespace Foam
-
 // ************************************************************************* //
diff --git a/src/triSurface/triSurface/interfaces/STL/readSTLBINARY.C b/src/triSurface/triSurface/interfaces/STL/readSTLBINARY.C
index 6f153c4e3a..e44ad78ddd 100644
--- a/src/triSurface/triSurface/interfaces/STL/readSTLBINARY.C
+++ b/src/triSurface/triSurface/interfaces/STL/readSTLBINARY.C
@@ -29,14 +29,10 @@ License
 #include "OSspecific.H"
 #include "gzstream.h"
 
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-namespace Foam
-{
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
-bool triSurface::readSTLBINARY(const fileName& STLfileName)
+bool Foam::triSurface::readSTLBINARY(const fileName& STLfileName)
 {
     bool compressed = false;
 
@@ -133,8 +129,4 @@ bool triSurface::readSTLBINARY(const fileName& STLfileName)
 }
 
 
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-} // End namespace Foam
-
 // ************************************************************************* //
diff --git a/src/triSurface/triSurface/interfaces/STL/writeSTL.C b/src/triSurface/triSurface/interfaces/STL/writeSTL.C
index 3abcb3dc9a..fd6eefd61e 100644
--- a/src/triSurface/triSurface/interfaces/STL/writeSTL.C
+++ b/src/triSurface/triSurface/interfaces/STL/writeSTL.C
@@ -29,14 +29,9 @@ License
 #include "HashTable.H"
 #include "hashSignedLabel.H"
 
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-namespace Foam
-{
-
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
-void triSurface::writeSTLASCII(Ostream& os) const
+void Foam::triSurface::writeSTLASCII(Ostream& os) const
 {
     labelList faceMap;
 
@@ -85,7 +80,7 @@ void triSurface::writeSTLASCII(Ostream& os) const
 }
 
 
-void triSurface::writeSTLBINARY(std::ostream& os) const
+void Foam::triSurface::writeSTLBINARY(std::ostream& os) const
 {
     // Write the STL header
     string header("Foam binary STL", STLheaderSize);
@@ -113,8 +108,4 @@ void triSurface::writeSTLBINARY(std::ostream& os) const
 }
 
 
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-} // End namespace Foam
-
 // ************************************************************************* //
diff --git a/src/triSurface/triSurface/stitchTriangles.C b/src/triSurface/triSurface/stitchTriangles.C
index 8771aeaec5..3e50995a2f 100644
--- a/src/triSurface/triSurface/stitchTriangles.C
+++ b/src/triSurface/triSurface/stitchTriangles.C
@@ -27,14 +27,9 @@ License
 #include "mergePoints.H"
 #include "PackedBoolList.H"
 
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-namespace Foam
-{
-
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
-bool triSurface::stitchTriangles
+bool Foam::triSurface::stitchTriangles
 (
     const pointField& rawPoints,
     const scalar tol,
@@ -114,11 +109,11 @@ bool triSurface::stitchTriangles
 
             forAll(*this, i)
             {
-                const labelledTri& tri = operator[](i);
+                const triSurface::FaceType& f = operator[](i);
 
-                forAll(tri, fp)
+                forAll(f, fp)
                 {
-                    label pointI = tri[fp];
+                    label pointI = f[fp];
                     if (pointIsUsed.set(pointI, 1))
                     {
                         nPoints++;
@@ -161,8 +156,4 @@ bool triSurface::stitchTriangles
 }
 
 
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-} // End namespace Foam
-
 // ************************************************************************* //
diff --git a/src/triSurface/triSurface/triSurface.C b/src/triSurface/triSurface/triSurface.C
index 399d0f6b35..4af0d616d4 100644
--- a/src/triSurface/triSurface/triSurface.C
+++ b/src/triSurface/triSurface/triSurface.C
@@ -187,20 +187,18 @@ void Foam::triSurface::checkTriangles(const bool verbose)
 
     forAll(*this, faceI)
     {
-        const labelledTri& f = (*this)[faceI];
+        const triSurface::FaceType& f = (*this)[faceI];
 
-        if
-        (
-            (f[0] < 0) || (f[0] > maxPointI)
-         || (f[1] < 0) || (f[1] > maxPointI)
-         || (f[2] < 0) || (f[2] > maxPointI)
-        )
+        forAll(f, fp)
         {
-            FatalErrorIn("triSurface::checkTriangles(bool)")
-                << "triangle " << f
-                << " uses point indices outside point range 0.."
-                << maxPointI
-                << exit(FatalError);
+            if (f[fp] < 0 || f[fp] > maxPointI)
+            {
+                FatalErrorIn("triSurface::checkTriangles(bool)")
+                    << "triangle " << f
+                    << " uses point indices outside point range 0.."
+                    << maxPointI
+                    << exit(FatalError);
+            }
         }
     }
 
@@ -960,42 +958,30 @@ void Foam::triSurface::subsetMeshMap
 
     boolList pointHad(nPoints(), false);
 
-    forAll(include, oldFacei)
+    forAll(include, oldFaceI)
     {
-        if (include[oldFacei])
+        if (include[oldFaceI])
         {
             // Store new faces compact
-            faceMap[faceI++] = oldFacei;
+            faceMap[faceI++] = oldFaceI;
 
-            // Renumber labels for triangle
-            const labelledTri& tri = locFaces[oldFacei];
+            // Renumber labels for face
+            const triSurface::FaceType& f = locFaces[oldFaceI];
 
-            label a = tri[0];
-            if (!pointHad[a])
+            forAll(f, fp)
             {
-                pointHad[a] = true;
-                pointMap[pointI++] = a;
-            }
-
-            label b = tri[1];
-            if (!pointHad[b])
-            {
-                pointHad[b] = true;
-                pointMap[pointI++] = b;
-            }
-
-            label c = tri[2];
-            if (!pointHad[c])
-            {
-                pointHad[c] = true;
-                pointMap[pointI++] = c;
+                label labI = f[fp];
+                if (!pointHad[labI])
+                {
+                    pointHad[labI] = true;
+                    pointMap[pointI++] = labI;
+                }
             }
         }
     }
 
     // Trim
     faceMap.setSize(faceI);
-
     pointMap.setSize(pointI);
 }
 
@@ -1086,9 +1072,9 @@ void Foam::triSurface::writeStats(Ostream& os) const
     label nPoints = 0;
     boundBox bb = boundBox::invertedBox;
 
-    forAll(*this, triI)
+    forAll(*this, faceI)
     {
-        const labelledTri& f = operator[](triI);
+        const triSurface::FaceType& f = operator[](faceI);
 
         forAll(f, fp)
         {
diff --git a/src/triSurface/triSurface/triSurfaceAddressing.C b/src/triSurface/triSurface/triSurfaceAddressing.C
index 0bdc2eb020..aabde66931 100644
--- a/src/triSurface/triSurface/triSurfaceAddressing.C
+++ b/src/triSurface/triSurface/triSurfaceAddressing.C
@@ -32,14 +32,10 @@ Description
 #include "SortableList.H"
 #include "transform.H"
 
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-namespace Foam
-{
 
 // * * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * //
 
-void triSurface::calcSortedEdgeFaces() const
+void Foam::triSurface::calcSortedEdgeFaces() const
 {
     if (sortedEdgeFacesPtr_)
     {
@@ -126,7 +122,7 @@ void triSurface::calcSortedEdgeFaces() const
 }
 
 
-void triSurface::calcEdgeOwner() const
+void Foam::triSurface::calcEdgeOwner() const
 {
     if (edgeOwnerPtr_)
     {
@@ -187,8 +183,4 @@ void triSurface::calcEdgeOwner() const
 }
 
 
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-} // End namespace Foam
-
 // ************************************************************************* //