Dodecadodecahedron

The dodecadodecahedron is a quasiregular uniform polyhedron. It consists of 12 pentagons and 12 pentagrams, with two of each joining at a vertex. It can be derived as a rectified small stellated dodecahedron or great dodecahedron.

Vertex coordinates
An icosidodecahedron of side length 1 has vertex coordinates given by all permutations of and even permutations of
 * (1, 0, 0),
 * (±(1+$\sqrt{5}$)/4, ±($\sqrt{5}$-1)/4, ±1/2).

The first set of vertices corresponds to a scaled octahedron which can be inscribed into the icosidodecahedron.