Rhombidodecadodecahedron

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Rhombidodecadodecahedron
Type	Uniform polyhedron
Elements	F=54, E=120, V=60 (χ=-6)
Faces by sides	30{4}+12{5}+12{5/2}
Wythoff symbol	5/2 5 | 2
Symmetry group	Ih
Index references	U38, C48, W76
4.5/2.4.5 (Vertex figure)	Medial deltoidal hexecontahedron (dual polyhedron)

In geometry, the rhombidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U₃₈.

By the Wythoff construction this polyhedra can also be named a cantellated great dodecahedron.

It shares its vertex arrangement with the uniform compounds of 10 or 20 triangular prisms.

[edit] Cartesian coordinates

Cartesian coordinates for the vertices of a uniform great rhombicosidodecahedron are all the even permutations of

(±1/τ², 0, ±τ²))

(±1, ±1, ±(2τ−1))

(±2, ±1/τ, ±τ)

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, Rhombidodecadodecahedron at MathWorld.