Rhombic triacontahedron

The rhombic triacontahedron, or rhote, is one of the 13 Catalan solids. It has 30 rhombi as faces, with 6 order-4 and 8 order-3 vertices. It is the dual of the uniform cuboctahedron.

The rhombic dodecahedron is the only Catalan solid that can tile 3D space by itself, forming the rhombic dodecahedral honeycomb.

Vertex coordinates
A rhombic dodecahedron of side length 1 has vertex coordinates given by all permutations of
 * (±$\sqrt{5+2√5}$/3, ±$\sqrt{3}$/3, ±$\sqrt{3}$/3),
 * (±2$\sqrt{3}$/3, 0, 0).