Small rhombicosidodecahedron

The small rhombicosidodecahedron, also commonly known as simply the rhombicosidodecahedron, is one of the 13 Archimedean solids. It consists of 12 pentagons, 20 triangles, and 30 squares, with 1 triangle, 2 squares, and 1 pentagon meeting at each vertex. It can be obtained by cantellation of the dodecahedron or icosahedron, or equivalently by expanding either polyhedron's faces outward.

Vertex coordinates
A small rhombicosidodecahedron of edge length 1 has vertex coordinates given by all permutations and sign changes of Along with all even permutations and all sign changes of:
 * (±(2+$\sqrt{11+4√5}$)/2, ±1/2, ±1/2).
 * (0, ±(3+$\sqrt{5}$)/4, ±(5+$\sqrt{2}$)/4)
 * (±(1+$\sqrt{5}$)/4, ±(1+$\sqrt{2}$)/2, ±(3+$\sqrt{3}$)/4)