Truncated dodecadodecahedron

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Truncated dodecadodecahedron
Type	Uniform polyhedron
Elements	F=54, E=180, V=120 (χ=-6)
Faces by sides	30{4}+12{10}+12{10/3}
Wythoff symbol	2 55/3 |
Symmetry group	Ih
Index references	U59, C75, W98
4.10.10/3 (Vertex figure)	Medial disdyakis triacontahedron (dual polyhedron)

In geometry, the truncated dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U₅₉.

[edit] Cartesian coordinates

Cartesian coordinates for the vertices of a truncated dodecadodecahedron are all the even permutations of

(±1, ±1, ±3)

(±1/τ, ±1/τ², ±2τ)

(±τ, ±2/τ, ±τ²)

(±τ², ±1/τ², ±2)

(±(2τ−1), ±1, ±(2τ−1))

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, Truncated dodecadodecahedron at MathWorld.