Rhombidodecadodecahedron

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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
Dual polyhedron Medial deltoidal hexecontahedron
Vertex figure Rhombidodecadodecahedron
4.5/2.4.5
Bowers acronym Raded


In geometry, the rhombidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U38. It is given a Schläfli symbol t0,2{5/2,5}, and by the Wythoff construction this polyhedron can also be named a cantellated great dodecahedron.

Cartesian coordinates[edit]

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).

Related polyhedra[edit]

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).

Rhombidodecadodecahedron convex hull.png
convex hull
Rhombidodecadodecahedron.png
Rhombidodecadodecahedron
Icosidodecadodecahedron.png
Icosidodecadodecahedron
Rhombicosahedron.png
Rhombicosahedron
UC32-10 triangular prisms.png
Compound of ten triangular prisms
UC33-20 triangular prisms.png
Compound of twenty triangular prisms

Medial deltoidal hexecontahedron[edit]

Medial deltoidal hexecontahedron
Rhombidodecadodecahedron
Type Star polyhedron
Face DU38 facets.png
Elements F = 60, E = 120
V = 54 (χ = −6)
Symmetry group Ih, [5,3], *532
Index references DU38
dual polyhedron Rhombidodecadodecahedron


The medial deltoidal hexecontahedron is a nonconvex isohedral polyhedron. It is the dual of the rhombidodecadodecahedron. It has 60 intersecting quadrilateral faces.

See also[edit]

References[edit]

External links[edit]