Icositruncated dodecadodecahedron

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Icositruncated dodecadodecahedron
Type	Uniform polyhedron
Elements	F=44, E=180, V=120 (χ=-16)
Faces by sides	20{6}+12{10}+12{10/3}
Wythoff symbol	3 55/3 |
Symmetry group	Ih
Index references	U45, C57, W84
6.10.10/3 (Vertex figure)	Tridyakis icosahedron (dual polyhedron)

In geometry, the icositruncated dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U₄₅.

[edit] Cartesian coordinates

Cartesian coordinates for the vertices of an icositruncated dodecadodecahedron are all the even permutations of

(±(2−1/τ), ±1, ±(2+τ))

(±1, ±1/τ², ±(3τ−1))

(±2, ±2/τ, ±2τ)

(±3, ±1/τ², ±τ²)

(±τ², ±1, ±(3τ−2))

where τ = (1+√5)/2 is the golden ratio (sometimes written φ).

[edit] See also

• List of uniform polyhedra

[edit] External links

• Eric W. Weisstein, Icositruncated dodecadodecahedron at MathWorld.