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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.
Contents
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).
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).
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.