Cantic cube
| Truncated tetrahedral graph | |
|---|---|
3-fold symmetry
|
|
| Vertices | 12 |
| Edges | 18 |
| Radius | 3 |
| Diameter | 3 |
| Girth | 3 |
| Automorphisms | 24 (S4) |
| Chromatic number | 3 |
| Chromatic index | 3 |
| Properties | Hamiltonian, regular, 3-vertex-connected, planar graph |
In geometry, the truncated tetrahedron is an Archimedean solid. It has 4 regular hexagonal faces, 4 equilateral triangle faces, 12 vertices and 18 edges (of two types). It can be constructed by truncating all 4 vertices of a regular tetrahedron at one third of the original edge length.
A deeper truncation, removing a tetrahedron of half the original edge length from each vertex, is called rectification. The rectification of a tetrahedron produces an octahedron.
A truncated tetrahedron is the Goldberg polyhedron GIII(1,1), containing triangular and hexagonal faces.
A truncated tetrahedron can be called a cantic cube, with Coxeter diagram, 
, having half of the vertices of the cantellated cube (rhombicuboctahedron), . There are two dual positions of this construction, and combining them creates the uniform compound of two truncated tetrahedra.
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