diff --git a/tests/CMakeLists.txt b/tests/CMakeLists.txt
index 2f8f4d42f7..bac6612df2 100644
--- a/tests/CMakeLists.txt
+++ b/tests/CMakeLists.txt
@@ -1046,6 +1046,52 @@ add_cmdline_test(offcgalpngtest        SCRIPT ${EX_IM_PNGTEST_PY} ARGS ${OPENSCA
 add_cmdline_test(dxfpngtest            SCRIPT ${EX_IM_PNGTEST_PY} ARGS ${OPENSCAD_ARG} --format=DXF --render=force EXPECTEDDIR cgalpngtest SUFFIX png FILES ${FILES_2D} ${SCAD_DXF_FILES})
 add_cmdline_test(svgpngtest            SCRIPT ${EX_IM_PNGTEST_PY} ARGS ${OPENSCAD_ARG} --format=SVG --render=force EXPECTEDDIR cgalpngtest SUFFIX png FILES ${FILES_2D} ${SCAD_SVG_FILES})
 
+# Manifold corner cases
+set(FILES_MANIFOLD_CORNER_CASES
+  ${TEST_SCAD_DIR}/3D/misc/tetracyl-slim.scad
+  ${TEST_SCAD_DIR}/3D/misc/tetracyl-touch-edge.scad
+  ${TEST_SCAD_DIR}/3D/misc/tetracyl-touch-edge-nonmanifold.scad
+  ${TEST_SCAD_DIR}/3D/misc/tetracyl-touch-vertex.scad
+  ${TEST_SCAD_DIR}/3D/misc/tetracyl-touch-vertex-nonmanifold.scad
+  ${TEST_SCAD_DIR}/3D/misc/polyhedrons-touch-edge-nonmanifold.scad
+  ${TEST_SCAD_DIR}/3D/misc/polyhedrons-touch-edge.scad
+  ${TEST_SCAD_DIR}/3D/misc/polyhedrons-touch-vertex-nonmanifold.scad
+  ${TEST_SCAD_DIR}/3D/misc/polyhedrons-touch-vertex.scad
+  ${TEST_SCAD_DIR}/3D/misc/polyhedrons-touch-face-nonmanifold.scad
+  ${TEST_SCAD_DIR}/3D/misc/polyhedrons-touch-face.scad
+  ${TEST_SCAD_DIR}/3D/misc/polyhedron-self-touch-edge-nonmanifold.scad
+  ${TEST_SCAD_DIR}/3D/misc/polyhedron-self-touch-edge.scad
+  ${TEST_SCAD_DIR}/3D/misc/polyhedron-self-touch-face-nonmanifold.scad
+  ${TEST_SCAD_DIR}/3D/misc/polyhedron-self-touch-face.scad
+  ${TEST_SCAD_DIR}/3D/misc/polyhedron-self-touch-vertex-nonmanifold.scad
+  ${TEST_SCAD_DIR}/3D/misc/polyhedron-self-touch-vertex.scad
+)
+add_cmdline_test(3mfpngtest SCRIPT ${EX_IM_PNGTEST_PY} ARGS ${OPENSCAD_ARG} --format=3MF --render=force EXPECTEDDIR 3mfpngtest SUFFIX png FILES ${FILES_MANIFOLD_CORNER_CASES})
+add_cmdline_test(objpngtest SCRIPT ${EX_IM_PNGTEST_PY} ARGS ${OPENSCAD_ARG} --format=OBJ --render=force EXPECTEDDIR 3mfpngtest SUFFIX png FILES ${FILES_MANIFOLD_CORNER_CASES})
+add_cmdline_test(offpngtest SCRIPT ${EX_IM_PNGTEST_PY} ARGS ${OPENSCAD_ARG} --format=OFF --render=force EXPECTEDDIR 3mfpngtest SUFFIX png FILES ${FILES_MANIFOLD_CORNER_CASES})
+add_cmdline_test(stlpngtest SCRIPT ${EX_IM_PNGTEST_PY} ARGS ${OPENSCAD_ARG} --format=STL --render=force EXPECTEDDIR 3mfpngtest SUFFIX png FILES ${FILES_MANIFOLD_CORNER_CASES})
+
+set_tests_properties(
+  # Manifold construction error. Probably due to polygon soup strategy
+  3mfpngtest_polyhedron-self-touch-face-nonmanifold
+  3mfpngtest_polyhedron-self-touch-face
+  objpngtest_polyhedron-self-touch-face-nonmanifold
+  objpngtest_polyhedron-self-touch-face
+  offpngtest_polyhedron-self-touch-face-nonmanifold
+  offpngtest_polyhedron-self-touch-face
+  stlpngtest_polyhedron-self-touch-face-nonmanifold
+  stlpngtest_polyhedron-self-touch-face
+	3mfpngtest_polyhedrons-touch-face-nonmanifold
+	3mfpngtest_polyhedrons-touch-face
+	objpngtest_polyhedrons-touch-face-nonmanifold
+	objpngtest_polyhedrons-touch-face
+	offpngtest_polyhedrons-touch-face-nonmanifold
+	offpngtest_polyhedrons-touch-face
+	stlpngtest_polyhedrons-touch-face-nonmanifold
+	stlpngtest_polyhedrons-touch-face
+  PROPERTIES DISABLED TRUE
+)
+
 # Failing tests
 add_failing_test(stlfailedtest         SUFFIX stl  FILES ${TEST_SCAD_DIR}/misc/empty-union.scad ARGS --retval=1)
 add_failing_test(offfailedtest         SUFFIX off  FILES ${TEST_SCAD_DIR}/misc/empty-union.scad ARGS --retval=1)
diff --git a/tests/data/scad/3D/misc/polyhedron-self-touch-edge-nonmanifold.scad b/tests/data/scad/3D/misc/polyhedron-self-touch-edge-nonmanifold.scad
new file mode 100644
index 0000000000..0777536bd6
--- /dev/null
+++ b/tests/data/scad/3D/misc/polyhedron-self-touch-edge-nonmanifold.scad
@@ -0,0 +1,33 @@
+// A single volume touching itself (two pairs of coincident vertices forming an edge).
+// This is a non-manifold object since the collapsed vertices are not distinct.
+polyhedron(
+  points=[
+    [0, 0, 0],
+    [1, 0, 0],
+    [0, 1, 0],
+    [1, 1, 0],
+
+    [0, 0, 1],
+    [1, 0, 1],
+    [0, 1, 1],
+    [1, 1, 1],
+
+    [0.4, 0.5, 0.5],
+    [0.6, 0.5, 0.5],
+  ],
+  faces=[
+    [5,4,8],[5,8,9],
+    [4,6,8],
+    [6,7,9],[6,9,8],
+    [7,5,9],
+    
+    [0,1,9],[0,9,8],
+    [1,3,9],
+    [3,2,8],[3,8,9],
+    [2,0,8],
+    
+    [4,5,1],[4,1,0],
+    [5,7,3],[5,3,1],
+    [7,6,2],[7,2,3],
+    [6,4,0],[6,0,2],
+  ]);
diff --git a/tests/data/scad/3D/misc/polyhedron-self-touch-edge.scad b/tests/data/scad/3D/misc/polyhedron-self-touch-edge.scad
new file mode 100644
index 0000000000..e5c4ac2c31
--- /dev/null
+++ b/tests/data/scad/3D/misc/polyhedron-self-touch-edge.scad
@@ -0,0 +1,36 @@
+// A single volume touching itself (two pairs of coincident vertices forming an edge),
+// but with a manifold topology (the coincident vertices are distinct).
+polyhedron(
+  points=[
+    [0, 0, 0],
+    [1, 0, 0],
+    [0, 1, 0],
+    [1, 1, 0],
+
+    [0, 0, 1],
+    [1, 0, 1],
+    [0, 1, 1],
+    [1, 1, 1],
+
+    [0.4, 0.5, 0.5],
+    [0.6, 0.5, 0.5],
+
+    [0.4, 0.5, 0.5],
+    [0.6, 0.5, 0.5],
+  ],
+  faces=[
+    [5,4,10],[5,10,11],
+    [4,6,10],
+    [6,7,11],[6,11,10],
+    [7,5,11],
+    
+    [0,1,9],[0,9,8],
+    [1,3,9],
+    [3,2,8],[3,8,9],
+    [2,0,8],
+    
+    [4,5,1],[4,1,0],
+    [5,7,3],[5,3,1],
+    [7,6,2],[7,2,3],
+    [6,4,0],[6,0,2],
+  ]);
diff --git a/tests/data/scad/3D/misc/polyhedron-self-touch-face-nonmanifold.scad b/tests/data/scad/3D/misc/polyhedron-self-touch-face-nonmanifold.scad
new file mode 100644
index 0000000000..3dd3c67062
--- /dev/null
+++ b/tests/data/scad/3D/misc/polyhedron-self-touch-face-nonmanifold.scad
@@ -0,0 +1,38 @@
+polyhedron(
+  points=[
+    [0, 0, 0],
+    [1, 0, 0],
+    [0, 1, 0],
+    [1, 1, 0],
+
+    [0, 0, 1],
+    [1, 0, 1],
+    [0, 1, 1],
+    [1, 1, 1],
+
+    [0.4, 0.4, 0.5],
+    [0.6, 0.4, 0.5],
+    [0.5, 0.6, 0.5],
+  ],
+  faces=[
+    [5,4,8],[5,8,9],
+    [4,6,8],
+    [6,10,8],
+    [6,7,10],
+    [7,9,10],
+    [7,5,9],
+    [10,9,8],
+    
+    [0,1,9],[0,9,8],
+    [1,3,9],
+    [3,10,9],
+    [3,2,10],
+    [2,8,10],
+    [2,0,8],
+    [8,9,10],
+    
+    [4,5,1],[4,1,0],
+    [5,7,3],[5,3,1],
+    [7,6,2],[7,2,3],
+    [6,4,0],[6,0,2],
+  ]);
diff --git a/tests/data/scad/3D/misc/polyhedron-self-touch-face.scad b/tests/data/scad/3D/misc/polyhedron-self-touch-face.scad
new file mode 100644
index 0000000000..064880ba29
--- /dev/null
+++ b/tests/data/scad/3D/misc/polyhedron-self-touch-face.scad
@@ -0,0 +1,43 @@
+// A single volume touching itself (three pairs of coincident vertices forming a triangle).
+polyhedron(
+  points=[
+    [0, 0, 0],
+    [1, 0, 0],
+    [0, 1, 0],
+    [1, 1, 0],
+
+    [0, 0, 1],
+    [1, 0, 1],
+    [0, 1, 1],
+    [1, 1, 1],
+
+    [0.4, 0.4, 0.5],
+    [0.6, 0.4, 0.5],
+    [0.5, 0.6, 0.5],
+
+    [0.4, 0.4, 0.5],
+    [0.6, 0.4, 0.5],
+    [0.5, 0.6, 0.5],
+  ],
+  faces=[
+    [5,4,11],[5,11,12]
+    [4,6,11],
+    [6,13,11],
+    [6,7,13],
+    [7,12,13],
+    [7,5,12],
+    [13,12,11],
+    
+    [0,1,9],[0,9,8],
+    [1,3,9],
+    [3,10,9],
+    [3,2,10],
+    [2,8,10],
+    [2,0,8],
+    [8,9,10],
+    
+    [4,5,1],[4,1,0],
+    [5,7,3],[5,3,1],
+    [7,6,2],[7,2,3],
+    [6,4,0,2],[6,0,2],
+  ]);
diff --git a/tests/data/scad/3D/misc/polyhedron-self-touch-vertex-nonmanifold.scad b/tests/data/scad/3D/misc/polyhedron-self-touch-vertex-nonmanifold.scad
new file mode 100644
index 0000000000..ea1e9ce9f1
--- /dev/null
+++ b/tests/data/scad/3D/misc/polyhedron-self-touch-vertex-nonmanifold.scad
@@ -0,0 +1,30 @@
+polyhedron(
+  points=[
+    [0, 0, 0],
+    [1, 0, 0],
+    [0, 1, 0],
+    [1, 1, 0],
+
+    [0, 0, 1],
+    [1, 0, 1],
+    [0, 1, 1],
+    [1, 1, 1],
+
+    [0.5, 0.5, 0.5],
+  ],
+  faces=[
+    [5,4,8],
+    [4,6,8],
+    [6,7,8],
+    [7,5,8],
+    
+    [0,1,8],
+    [1,3,8],
+    [3,2,8],
+    [2,0,8],
+    
+    [4,5,1],[4,1,0],
+    [5,7,3],[5,3,1],
+    [7,6,2],[7,2,3],
+    [6,4,0],[6,0,2],
+  ]);
diff --git a/tests/data/scad/3D/misc/polyhedron-self-touch-vertex.scad b/tests/data/scad/3D/misc/polyhedron-self-touch-vertex.scad
new file mode 100644
index 0000000000..f8e0dc9175
--- /dev/null
+++ b/tests/data/scad/3D/misc/polyhedron-self-touch-vertex.scad
@@ -0,0 +1,31 @@
+polyhedron(
+  points=[
+    [0, 0, 0],
+    [1, 0, 0],
+    [0, 1, 0],
+    [1, 1, 0],
+
+    [0, 0, 1],
+    [1, 0, 1],
+    [0, 1, 1],
+    [1, 1, 1],
+
+    [0.5, 0.5, 0.5],
+    [0.5, 0.5, 0.5],
+  ],
+  faces=[
+    [5,4,9],
+    [4,6,9],
+    [6,7,9],
+    [7,5,9],
+    
+    [0,1,8],
+    [1,3,8],
+    [3,2,8],
+    [2,0,8],
+    
+    [4,5,1],[4,1,0],
+    [5,7,3],[5,3,1],
+    [7,6,2],[7,2,3],
+    [6,4,0],[6,0,2],
+  ]);
diff --git a/tests/data/scad/3D/misc/polyhedrons-touch-edge-nonmanifold.scad b/tests/data/scad/3D/misc/polyhedrons-touch-edge-nonmanifold.scad
new file mode 100644
index 0000000000..783840e4a4
--- /dev/null
+++ b/tests/data/scad/3D/misc/polyhedrons-touch-edge-nonmanifold.scad
@@ -0,0 +1,34 @@
+// Two cubes sharing an edge.
+// This is a non-manifold object since the collapsed vertices are not distinct.
+polyhedron(
+  points=[
+    [0, 0, 0],
+    [1, 0, 0],
+    [0, 1, 0],
+    [1, 1, 0],
+    [0, 0, 1],
+    [1, 0, 1],
+    [0, 1, 1],
+    [1, 1, 1],
+
+    [2, 1, 0],
+    [1, 2, 0],
+    [2, 2, 0],
+    [2, 1, 1],
+    [1, 2, 1],
+    [2, 2, 1],
+  ],
+  faces=[
+    [6,7,5,4],
+    [0,1,3,2],
+    [4,5,1,0],
+    [5,7,3,1],
+    [7,6,2,3],
+    [6,4,0,2],
+    [12,13,11,7],
+    [3,8,10,9],
+    [7,11,8,3],
+    [11,13,10,8],
+    [13,12,9,10],
+    [12,7,3,9],
+  ]);
diff --git a/tests/data/scad/3D/misc/polyhedrons-touch-edge.scad b/tests/data/scad/3D/misc/polyhedrons-touch-edge.scad
new file mode 100644
index 0000000000..f40f314301
--- /dev/null
+++ b/tests/data/scad/3D/misc/polyhedrons-touch-edge.scad
@@ -0,0 +1,34 @@
+polyhedron(
+  points=[
+    [0, 0, 0],
+    [1, 0, 0],
+    [0, 1, 0],
+    [1, 1, 0],
+    [0, 0, 1],
+    [1, 0, 1],
+    [0, 1, 1],
+    [1, 1, 1],
+
+    [1, 1, 0],
+    [2, 1, 0],
+    [1, 2, 0],
+    [2, 2, 0],
+    [1, 1, 1],
+    [2, 1, 1],
+    [1, 2, 1],
+    [2, 2, 1],
+  ],
+  faces=[
+    [6,7,5],[6,5,4],
+    [0,1,3],[0,3,2],
+    [4,5,1],[4,1,0],
+    [5,7,3],[5,3,1],
+    [7,6,2],[7,2,3],
+    [6,4,0],[6,0,2],
+    [14,15,13],[14,13,7],
+    [3,9,11],[3,11,10],
+    [7,13,9],[7,9,3],
+    [13,15,11],[13,11,9],
+    [15,14,10],[15,10,11],
+    [14,7,3],[14,3,10],
+  ]);
diff --git a/tests/data/scad/3D/misc/polyhedrons-touch-face-nonmanifold.scad b/tests/data/scad/3D/misc/polyhedrons-touch-face-nonmanifold.scad
new file mode 100644
index 0000000000..4cdb11848e
--- /dev/null
+++ b/tests/data/scad/3D/misc/polyhedrons-touch-face-nonmanifold.scad
@@ -0,0 +1,30 @@
+polyhedron(
+  points=[
+    [0, 0, 0],
+    [1, 0, 0],
+    [0, 1, 0],
+    [1, 1, 0],
+    [0, 0, 1],
+    [1, 0, 1],
+    [0, 1, 1],
+    [1, 1, 1],
+
+    [2, 0, 0],
+    [2, 1, 0],
+    [2, 0, 1],
+    [2, 1, 1],
+  ],
+  faces=[
+    [6,7,5],[6,5,4],
+    [0,1,3],[0,3,2],
+    [4,5,1],[4,1,0],
+    [5,7,3],[5,3,1],
+    [7,6,2],[7,2,3],
+    [4,0,2],[4,2,6],
+    [7,11,10],[7,10,5],
+    [1,8,9],[1,9,3],
+    [5,10,8],[5,8,1],
+    [10,11,9],[10,9,8],
+    [11,7,3],[11,3,9],
+    [5,1,3],[5,3,7],
+  ]);
diff --git a/tests/data/scad/3D/misc/polyhedrons-touch-face.scad b/tests/data/scad/3D/misc/polyhedrons-touch-face.scad
new file mode 100644
index 0000000000..7adc331a83
--- /dev/null
+++ b/tests/data/scad/3D/misc/polyhedrons-touch-face.scad
@@ -0,0 +1,36 @@
+// Two cubes sharing a face,
+// but with a manifold topology (the coincident vertices are distinct).
+polyhedron(
+  points=[
+    [0, 0, 0],
+    [1, 0, 0],
+    [0, 1, 0],
+    [1, 1, 0],
+    [0, 0, 1],
+    [1, 0, 1],
+    [0, 1, 1],
+    [1, 1, 1],
+
+    [1, 0, 0],
+    [2, 0, 0],
+    [1, 1, 0],
+    [2, 1, 0],
+    [1, 0, 1],
+    [2, 0, 1],
+    [1, 1, 1],
+    [2, 1, 1],
+  ],
+  faces=[
+    [6,7,5],[6,5,4],
+    [0,1,3],[0,3,2],
+    [4,5,1],[4,1,0],
+    [5,7,3],[5,3,1],
+    [7,6,2],[7,2,3],
+    [4,0,2],[4,2,6],
+    [14,15,13],[14,13,12],
+    [8,9,11],[8,11,10],
+    [12,13,9],[12,9,8],
+    [13,15,11],[13,11,9],
+    [15,14,10],[15,10,11],
+    [12,8,10],[12,10,14],
+  ]);
diff --git a/tests/data/scad/3D/misc/polyhedrons-touch-vertex-nonmanifold.scad b/tests/data/scad/3D/misc/polyhedrons-touch-vertex-nonmanifold.scad
new file mode 100644
index 0000000000..d477b3e7f8
--- /dev/null
+++ b/tests/data/scad/3D/misc/polyhedrons-touch-vertex-nonmanifold.scad
@@ -0,0 +1,36 @@
+// Two cubes sharing a vertex.
+// This is a non-manifold object since the collapsed vertices are not distinct.
+polyhedron(
+  points=[
+    [0, 0, 0],
+    [1, 0, 0],
+    [0, 1, 0],
+    [1, 1, 0],
+    [0, 0, 1],
+    [1, 0, 1],
+    [0, 1, 1],
+    [1, 1, 1],
+
+    [2, 1, 1],
+    [1, 2, 1],
+    [2, 2, 1],
+    [1, 1, 2],
+    [2, 1, 2],
+    [1, 2, 2],
+    [2, 2, 2],
+  ],
+  faces=[
+    [6,7,5],[6,5,4],
+    [0,1,3],[0,3,2],
+    [4,5,1],[4,1,0],
+    [5,7,3],[5,3,1],
+    [7,6,2],[7,2,3],
+    [6,4,0],[6,0,2],
+
+    [13,14,12],[13,12,11],
+    [7,8,10],[7,10,9],
+    [11,12,8],[11,8,7],
+    [12,14,10],[12,10,8],
+    [14,13,9],[14,9,10],
+    [13,11,7],[13,7,9],
+  ]);
diff --git a/tests/data/scad/3D/misc/polyhedrons-touch-vertex.scad b/tests/data/scad/3D/misc/polyhedrons-touch-vertex.scad
new file mode 100644
index 0000000000..d90d8f9bb4
--- /dev/null
+++ b/tests/data/scad/3D/misc/polyhedrons-touch-vertex.scad
@@ -0,0 +1,35 @@
+// Two cubes sharing a vertex,
+// but with a manifold topology (the coincident vertices are distinct).
+polyhedron(
+  points=[
+    [0, 0, 0],
+    [1, 0, 0],
+    [0, 1, 0],
+    [1, 1, 0],
+    [0, 0, 1],
+    [1, 0, 1],
+    [0, 1, 1],
+    [1, 1, 1],
+    [1, 1, 1],
+    [2, 1, 1],
+    [1, 2, 1],
+    [2, 2, 1],
+    [1, 1, 2],
+    [2, 1, 2],
+    [1, 2, 2],
+    [2, 2, 2],
+  ],
+  faces=[
+    [6,7,5],[6,5,4],
+    [0,1,3],[0,3,2],
+    [4,5,1],[4,1,0],
+    [5,7,3],[5,3,1],
+    [7,6,2],[7,2,3],
+    [6,4,0],[6,0,2],
+    [14,15,13],[14,13,12],
+    [8,9,11],[8,11,10],
+    [12,13,9],[12,9,8],
+    [13,15,11],[13,11,9],
+    [15,14,10],[15,10,11],
+    [14,12,8],[14,8,10],
+  ]);
diff --git a/tests/data/scad/3D/misc/tetracyl-slim.scad b/tests/data/scad/3D/misc/tetracyl-slim.scad
new file mode 100644
index 0000000000..8082e4adf2
--- /dev/null
+++ b/tests/data/scad/3D/misc/tetracyl-slim.scad
@@ -0,0 +1,28 @@
+h = 1;
+
+// A cylinder with a triangular base and a slim waist
+polyhedron(
+  points=[
+    [0,1,0],
+    [cos(210), sin(210),0],
+    [cos(330), sin(330),0],
+
+    [0,0.1,h],
+    [0.1*cos(210), 0.1*sin(210),h],
+    [0.1*cos(330), 0.1*sin(330),h],
+
+    [0,1,2*h],
+    [cos(210), sin(210),2*h],
+    [cos(330), sin(330),2*h],
+  ],
+  faces=[
+    [0,1,2],
+    [1,0,3],[1,3,4],
+    [0,2,5],[0,5,3],
+    [2,1,4],[2,4,5],
+
+    [4,3,6],[4,6,7],
+    [5,4,7],[5,7,8],
+    [3,5,8],[3,8,6],
+    [8,7,6],
+  ]);
diff --git a/tests/data/scad/3D/misc/tetracyl-touch-edge-nonmanifold.scad b/tests/data/scad/3D/misc/tetracyl-touch-edge-nonmanifold.scad
new file mode 100644
index 0000000000..0154d21222
--- /dev/null
+++ b/tests/data/scad/3D/misc/tetracyl-touch-edge-nonmanifold.scad
@@ -0,0 +1,28 @@
+h = 1;
+
+// A cylinder with a triangular base and a slim waist which is collapsed into a single edge.
+// This is a non-manifold object since the collapsed vertices are not distinct.
+polyhedron(
+  points=[
+    [0,1,0],
+    [cos(210), sin(210),0],
+    [cos(330), sin(330),0],
+
+    [0,0.1,h],
+    [0.1*cos(270), 0.1*sin(270),h],
+
+    [0,1,2*h],
+    [cos(210), sin(210),2*h],
+    [cos(330), sin(330),2*h],
+  ],
+  faces=[
+    [0,1,2],
+    [1,0,3],[1,3,4],
+    [0,2,4],[0,4,3],
+    [2,1,4],
+
+    [4,3,5],[4,5,6],
+    [4,6,7],
+    [3,4,7],[3,7,5],
+    [7,6,5],
+  ]);
diff --git a/tests/data/scad/3D/misc/tetracyl-touch-edge.scad b/tests/data/scad/3D/misc/tetracyl-touch-edge.scad
new file mode 100644
index 0000000000..5bd4426602
--- /dev/null
+++ b/tests/data/scad/3D/misc/tetracyl-touch-edge.scad
@@ -0,0 +1,29 @@
+h = 1;
+
+// A cylinder with a triangular base and a slim waist which is collapsed into a single edge,
+// but with a manifold topology (the collapsed vertices are still distinct).
+polyhedron(
+  points=[
+    [0,1,0],
+    [cos(210), sin(210),0],
+    [cos(330), sin(330),0],
+
+    [0,0.1,h],
+    [0.1*cos(270), 0.1*sin(270),h],
+    [0.1*cos(270), 0.1*sin(270),h],
+
+    [0,1,2*h],
+    [cos(210), sin(210),2*h],
+    [cos(330), sin(330),2*h],
+  ],
+  faces=[
+    [0,1,2],
+    [1,0,3],[1,3,4],
+    [0,2,5],[0,5,3],
+    [2,1,4],[2,4,5],
+
+    [4,3,6],[4,6,7],
+    [5,4,7],[5,7,8],
+    [3,5,8],[3,8,6],
+    [8,7,6],
+  ]);
diff --git a/tests/data/scad/3D/misc/tetracyl-touch-vertex-nonmanifold.scad b/tests/data/scad/3D/misc/tetracyl-touch-vertex-nonmanifold.scad
new file mode 100644
index 0000000000..90920963e3
--- /dev/null
+++ b/tests/data/scad/3D/misc/tetracyl-touch-vertex-nonmanifold.scad
@@ -0,0 +1,27 @@
+h = 1;
+
+// A cylinder with a triangular base and a slim waist which is collapsed into a single vertex.
+// This is a non-manifold object since the collapsed vertices are not distinct.
+polyhedron(
+  points=[
+    [0,1,0],
+    [cos(210), sin(210),0],
+    [cos(330), sin(330),0],
+
+    [0,0,h],
+
+    [0,1,2*h],
+    [cos(210), sin(210),2*h],
+    [cos(330), sin(330),2*h],
+  ],
+  faces=[
+    [0,1,2],
+    [1,0,3],
+    [0,2,3],
+    [2,1,3],
+
+    [3,4,5],
+    [3,5,6],
+    [3,6,4],
+    [6,5,4],
+  ]);
diff --git a/tests/data/scad/3D/misc/tetracyl-touch-vertex.scad b/tests/data/scad/3D/misc/tetracyl-touch-vertex.scad
new file mode 100644
index 0000000000..d900b3777c
--- /dev/null
+++ b/tests/data/scad/3D/misc/tetracyl-touch-vertex.scad
@@ -0,0 +1,29 @@
+h = 1;
+
+// A cylinder with a triangular base and a slim waist which is collapsed into a single vertex,
+// but with a manifold topology (the collapsed vertices are still distinct).
+polyhedron(
+  points=[
+    [0,1,0],
+    [cos(210), sin(210),0],
+    [cos(330), sin(330),0],
+
+    [0,0,h],
+    [0,0,h],
+    [0,0,h],
+
+    [0,1,2*h],
+    [cos(210), sin(210),2*h],
+    [cos(330), sin(330),2*h],
+  ],
+  faces=[
+    [0,1,2],
+    [1,0,3],[1,3,4],
+    [0,2,5],[0,5,3],
+    [2,1,4],[2,4,5],
+
+    [4,3,6],[4,6,7],
+    [5,4,7],[5,7,8],
+    [3,5,8],[3,8,6],
+    [8,7,6],
+  ]);
diff --git a/tests/regression/3mfpngtest/polyhedron-self-touch-edge-expected.png b/tests/regression/3mfpngtest/polyhedron-self-touch-edge-expected.png
new file mode 100644
index 0000000000..8795f6580c
Binary files /dev/null and b/tests/regression/3mfpngtest/polyhedron-self-touch-edge-expected.png differ
diff --git a/tests/regression/3mfpngtest/polyhedron-self-touch-edge-nonmanifold-expected.png b/tests/regression/3mfpngtest/polyhedron-self-touch-edge-nonmanifold-expected.png
new file mode 100644
index 0000000000..8795f6580c
Binary files /dev/null and b/tests/regression/3mfpngtest/polyhedron-self-touch-edge-nonmanifold-expected.png differ
diff --git a/tests/regression/3mfpngtest/polyhedron-self-touch-face-expected.png b/tests/regression/3mfpngtest/polyhedron-self-touch-face-expected.png
new file mode 100644
index 0000000000..e69de29bb2
diff --git a/tests/regression/3mfpngtest/polyhedron-self-touch-face-nonmanifold-expected.png b/tests/regression/3mfpngtest/polyhedron-self-touch-face-nonmanifold-expected.png
new file mode 100644
index 0000000000..e69de29bb2
diff --git a/tests/regression/3mfpngtest/polyhedron-self-touch-vertex-expected.png b/tests/regression/3mfpngtest/polyhedron-self-touch-vertex-expected.png
new file mode 100644
index 0000000000..1f0572671a
Binary files /dev/null and b/tests/regression/3mfpngtest/polyhedron-self-touch-vertex-expected.png differ
diff --git a/tests/regression/3mfpngtest/polyhedron-self-touch-vertex-nonmanifold-expected.png b/tests/regression/3mfpngtest/polyhedron-self-touch-vertex-nonmanifold-expected.png
new file mode 100644
index 0000000000..1f0572671a
Binary files /dev/null and b/tests/regression/3mfpngtest/polyhedron-self-touch-vertex-nonmanifold-expected.png differ
diff --git a/tests/regression/3mfpngtest/polyhedrons-touch-edge-expected.png b/tests/regression/3mfpngtest/polyhedrons-touch-edge-expected.png
new file mode 100644
index 0000000000..e98969b744
Binary files /dev/null and b/tests/regression/3mfpngtest/polyhedrons-touch-edge-expected.png differ
diff --git a/tests/regression/3mfpngtest/polyhedrons-touch-edge-nonmanifold-expected.png b/tests/regression/3mfpngtest/polyhedrons-touch-edge-nonmanifold-expected.png
new file mode 100644
index 0000000000..e98969b744
Binary files /dev/null and b/tests/regression/3mfpngtest/polyhedrons-touch-edge-nonmanifold-expected.png differ
diff --git a/tests/regression/3mfpngtest/polyhedrons-touch-face-expected.png b/tests/regression/3mfpngtest/polyhedrons-touch-face-expected.png
new file mode 100644
index 0000000000..f1c7975030
Binary files /dev/null and b/tests/regression/3mfpngtest/polyhedrons-touch-face-expected.png differ
diff --git a/tests/regression/3mfpngtest/polyhedrons-touch-face-nonmanifold-expected.png b/tests/regression/3mfpngtest/polyhedrons-touch-face-nonmanifold-expected.png
new file mode 100644
index 0000000000..8c4ac38779
Binary files /dev/null and b/tests/regression/3mfpngtest/polyhedrons-touch-face-nonmanifold-expected.png differ
diff --git a/tests/regression/3mfpngtest/polyhedrons-touch-vertex-expected.png b/tests/regression/3mfpngtest/polyhedrons-touch-vertex-expected.png
new file mode 100644
index 0000000000..3fad684c1a
Binary files /dev/null and b/tests/regression/3mfpngtest/polyhedrons-touch-vertex-expected.png differ
diff --git a/tests/regression/3mfpngtest/polyhedrons-touch-vertex-nonmanifold-expected.png b/tests/regression/3mfpngtest/polyhedrons-touch-vertex-nonmanifold-expected.png
new file mode 100644
index 0000000000..3fad684c1a
Binary files /dev/null and b/tests/regression/3mfpngtest/polyhedrons-touch-vertex-nonmanifold-expected.png differ
diff --git a/tests/regression/3mfpngtest/tetracyl-slim-expected.png b/tests/regression/3mfpngtest/tetracyl-slim-expected.png
new file mode 100644
index 0000000000..264842eb71
Binary files /dev/null and b/tests/regression/3mfpngtest/tetracyl-slim-expected.png differ
diff --git a/tests/regression/3mfpngtest/tetracyl-touch-edge-expected.png b/tests/regression/3mfpngtest/tetracyl-touch-edge-expected.png
new file mode 100644
index 0000000000..c17b96f0a0
Binary files /dev/null and b/tests/regression/3mfpngtest/tetracyl-touch-edge-expected.png differ
diff --git a/tests/regression/3mfpngtest/tetracyl-touch-edge-nonmanifold-expected.png b/tests/regression/3mfpngtest/tetracyl-touch-edge-nonmanifold-expected.png
new file mode 100644
index 0000000000..c17b96f0a0
Binary files /dev/null and b/tests/regression/3mfpngtest/tetracyl-touch-edge-nonmanifold-expected.png differ
diff --git a/tests/regression/3mfpngtest/tetracyl-touch-vertex-expected.png b/tests/regression/3mfpngtest/tetracyl-touch-vertex-expected.png
new file mode 100644
index 0000000000..7afa3837e5
Binary files /dev/null and b/tests/regression/3mfpngtest/tetracyl-touch-vertex-expected.png differ
diff --git a/tests/regression/3mfpngtest/tetracyl-touch-vertex-nonmanifold-expected.png b/tests/regression/3mfpngtest/tetracyl-touch-vertex-nonmanifold-expected.png
new file mode 100644
index 0000000000..7afa3837e5
Binary files /dev/null and b/tests/regression/3mfpngtest/tetracyl-touch-vertex-nonmanifold-expected.png differ