Chamfered tetrahedron
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| Chamfered tetrahedron | |
|---|---|
 | |
| Rank | 3 |
| Elements | |
| Faces | 4 triangles, 6 point-symmetric hexagons |
| Edges | 12+12 |
| Vertices | 4+12 |
| Vertex figures | 4 equilateral triangles |
| 12 isosceles triangles | |
| Measures (edge length 1) | |
| Dihedral angles | 3-6: |
| 6-6: 90° | |
| Central density | 1 |
| Number of external pieces | 10 |
| Level of complexity | 4 |
| Related polytopes | |
| Army | Chamfered tetrahedron |
| Regiment | Chamfered tetrahedron |
| Dual | Alternate-triakis tetratetrahedron |
| Conjugate | None |
| Abstract & topological properties | |
| Euler characteristic | 2 |
| Surface | Sphere |
| Orientable | Yes |
| Genus | 0 |
| Properties | |
| Symmetry | A3, order 24 |
| Convex | Yes |
| Nature | Tame |
The chamfered tetrahedron is a modification of the tetrahedron that can have one edge length but has irregular faces. It has 4 triangles and 6 hexagons as faces, and 4 order-3 vertices that can be thought of as coming from the tetrahedron as well as 12 new order-3 vertices.
The hexagonal faces have angles of 90° on one pair of opposite vertices, and angles of 135° on the four remaining vertices.
It can be modified such that it has a single inradius, or such that it has a single midradius or "edge radius." The latter version is called the "canonical" version.
It can also be obtained by truncating alternate vertices of a cube, and can also be viewed as a tetrahedrally-symmetric Goldberg polyhedron.
External links[edit | edit source]
- Klitzing, Richard. "patex cube".
- Wikipedia contributors. "Chamfered tetrahedron".
- McCooey, David. "Chamfered Tetrahedron (all edges equal)"