Icosidodecahedron

The icosidodecahedron is a quasiregular polyhedron and one of the 13 Archimedian solids. It consists of 12 pentagons and 20 equilateral triangles, with two of each joining at a vertex. It can be derived as a rectified dodecahedron or icosahedron.

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

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