There are two nonconvex forms, the tetrahemihexahedron and octahemioctahedron which have tetrahedral symmetry (with fundamental domain Möbius triangle (3 3 2)).
There are two Schwarz triangles that generate unique nonconvex uniform polyhedra: one right triangle (3/2 3 2), and one general triangle (3/2 3 3).
| Vertex arrangement (Convex hull) |
Nonconvex forms | |
|---|---|---|
Tetrahedron |
||
Rectified tetrahedron Octahedron |
(4.3/2.4.3) 3/2 3 | 2 |
|
Truncated tetrahedron |
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Cantellated tetrahedron (Cuboctahedron) |
(6.3/2.6.3) 3/2 3 | 3 |
|
Omnitruncated tetrahedron (Truncated octahedron) |
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Snub tetrahedron (Icosahedron) |
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Read more about this topic: Nonconvex Polyhedra
Famous quotes containing the word symmetry:
“What makes a regiment of soldiers a more noble object of view than the same mass of mob? Their arms, their dresses, their banners, and the art and artificial symmetry of their position and movements.”
—George Gordon Noel Byron (1788–1824)