Rhombidodecadodecahedron

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

(±1/τ², 0, ±τ²)

(±1, ±1, ±√5)

(±2, ±1/τ, ±τ)

where τ = (1+√5)/2 is the golden ratio (sometimes written φ).

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

Medial deltoidal hexecontahedron

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

3D model of a medial deltoidal hexecontahedron

The medial deltoidal hexecontahedron (or midly lanceal ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the rhombidodecadodecahedron. It has 60 intersecting quadrilateral faces.

• List of uniform polyhedra

• Wenninger, Magnus (1983), Dual Models, Cambridge University Press, doi:10.1017/CBO9780511569371, ISBN 978-0-521-54325-5, MR 0730208

• Weisstein, Eric W. "Rhombidodecadodecahedron". MathWorld.
• Weisstein, Eric W. "Medial deltoidal hexecontahedron". MathWorld.
• Uniform polyhedra and duals