Rhombidodecadodecahedron

Rhombidodecadodecahedron
Type	Uniform star 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, [5,3], *532
Index references	U38, C48, W76
Bowers acronym	Raded
4.5/2.4.5 (Vertex figure)	Medial deltoidal hexecontahedron (dual polyhedron)

In geometry, the rhombidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U₃₈. It is given a Schläfli symbol t_0,2{5/2,5}, and by the Wythoff construction this polyhedron can also be named a cantellated great dodecahedron.

Related polyhedra

It shares its vertex arrangement with the uniform compounds of 10 or 20 triangular prisms. It additionally shares its edges with the icosidodecadodecahedron (having the pentagonal and pentagrammic faces in common) and the rhombicosahedron (having the square faces in common).

convex hull	Rhombidodecadodecahedron	Icosidodecadodecahedron
Rhombicosahedron	Compound of ten triangular prisms	Compound of twenty triangular prisms

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).

See also

• List of uniform polyhedra

External links

• Weisstein, Eric W., "Rhombidodecadodecahedron" from MathWorld.
• Uniform polyhedra and duals