Truncated dodecahedron
| Truncated dodecahedral graph | |
|---|---|
5-fold symmetry schlegel diagram
|
|
| Vertices | 60 |
| Edges | 90 |
| Automorphisms | 120 |
| Chromatic number | 2 |
| Properties | Cubic, Hamiltonian, regular, zero-symmetric |
In geometry, the truncated dodecahedron is an Archimedean solid. It has 12 regular decagonal faces, 20 regular triangular faces, 60 vertices and 90 edges.
This polyhedron can be formed from a dodecahedron by truncating (cutting off) the corners so the pentagon faces become decagons and the corners become triangles.
It is used in the cell-transitive hyperbolic space-filling tessellation, the bitruncated icosahedral honeycomb.
The area A and the volume V of a truncated dodecahedron of edge length a are:
Cartesian coordinates for the vertices of a truncated dodecahedron with edge length 2φ − 2, centered at the origin, are all even permutations of:
where φ = 1 + √5/2 is the golden ratio.
The truncated dodecahedron has five special orthogonal projections, centered, on a vertex, on two types of edges, and two types of faces: hexagonal and pentagonal. The last two correspond to the A2 and H2Coxeter planes.
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