rhombicosidodecahedron

It can be obtained as a slice of the rhombicosidodecahedron.

It can also be constructed as a rectified rhombicosidodecahedron.

It is the dual of the nonconvex great rhombicosidodecahedron.

A further alternation step leads to the snub rhombicosidodecahedron.

It can be constructed as a rhombicosidodecahedron with two opposing pentagonal cupolae removed.

The original dodecahedron cells are cantitruncated into great rhombicosidodecahedron cells.

This model shares the name with the convex great rhombicosidodecahedron, also known as the truncated icosidodecahedron.

In the picture of the small complex rhombicosidodecahedron, the pentagrams are pink, the squares red, and the triangles yellow.

In geometry, the diminished rhombicosidodecahedron is one of the Johnson solids (J).

It can be constructed as a rhombicosidodecahedron with one pentagonal cupola rotated through 36 degrees.

Alternative Johnson solids, constructed by rotating different cupolae of a rhombicosidodecahedron, are:

Compare to small rhombicosidodecahedron.

The truncated rhombicosidodecahedron can be seen in sequence of rectification and truncation operations from the icosidodecahedron.

J: tridiminished rhombicosidodecahedron with three cupola removed.

Specifically, a rhombicosidodecahedron.

See nonconvex great rhombicosidodecahedron.

J: metabidiminished rhombicosidodecahedron with two non-opposing cupolae removed.

The rhombicosidodecahedron can also be represented as a spherical tiling, and projected onto the plane via a stereographic projection.

The truncated dodecahedron, rhombicosidodecahedron, and truncated icosahedron as degenerate limiting cases.

World of Polyhedra - metabigyrate rhombicosidodecahedron (interactive rotatable wireframe applet)

The centres of the pentagrams have been removed as otherwise the red squares of the small complex rhombicosidodecahedron would be invisible.)

In geometry, the nonconvex great rhombicosidodecahedron is a nonconvex uniform polyhedron, indexed as U.

The pentagrammic cuploid may be seen as a section of the degenerate uniform polyhedron known as the small complex rhombicosidodecahedron:

Great rhombicosidodecahedron (Robert Williams, Peter Cromwell)

Cartesian coordinates for the vertices of a rhombicosidodecahedron with edge length 2 centered at the origin are all even permutations of: