Icosahedron - Uniform Colorings and Subsymmetries

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)

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