Rhombidodecadodecahedron


In geometry, the rhombidodecadodecahedron is a nonconvex uniform polyhedron, indexed as U38. It has 54 faces, 120 edges and 60 vertices. It is given a Schläfli symbol t0,2{,5}, and by the Wythoff construction this polyhedron can also be named a cantellated great dodecahedron.

Cartesian coordinates

for the vertices of a uniform great rhombicosidodecahedron are all the even permutations of
where τ = /2 is the golden ratio.

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 and the rhombicosahedron.

convex hull
Rhombidodecadodecahedron
Icosidodecadodecahedron

Rhombicosahedron
Compound of ten triangular prisms
Compound of twenty triangular prisms

Medial deltoidal hexecontahedron

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