Great icosidodecahedron

The great icosidodecahedron is a quasiregular uniform polyhedron. It consists of 20 equilateral triangles and 12 pentagrams, with two of each joining at a vertex. It can be derived as a rectified great stellated dodecahedron or great icosahedron.

Vertex coordinates
An icosidodecahedron of side length 1 has vertex coordinates given by all permutations of and even permutations of
 * (±($\sqrt{5}$–1)/2, 0, 0),
 * (±(3–$\sqrt{5}$)/4, ±($\sqrt{5}$–1)/4, ±1/2).

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