Uniform Colorings and Subsymmetries
There are 3 uniform colorings of the icosahedron. These colorings can be represented as 11213, 11212, 11111, naming the 5 triangular faces around each vertex by their color.
The icosahedron can be considered a snub tetrahedron, as snubification of a regular tetrahedron gives a regular icosahedron having chiral tetrahedral symmetry. It can also be constructed as an alternated truncated octahedron, having pyritohedral symmetry. The pyritohedral symmetry version is sometimes called a pseudoicosahedron, and is dual to the pyritohedron.
| Name | Regular icosahedron | alternated truncated octahedron |
snub tetrahedron |
Pentagonal gyroelongated bipyramid |
|---|---|---|---|---|
| Coxeter-Dynkin | ||||
| Schläfli symbol | {3,5} | h0,1{3,4} | s{3,3} | |
| Wythoff symbol | 5 | 3 2 | | 3 3 2 | ||
| Symmetry | Ih (*532) |
Th (3*2) |
T + (332) |
D5d (2*5) |
| Symmetry order | 60 | 24 | 12 | 10 |
| Uniform coloring | (11111) |
(11212) |
(11213) |
(11122)&(22222) |
Read more about this topic: Icosahedron
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