For a rhombicosidodecahedron with edge length a, its surface area and volume are: If you expand an icosidodecahedron by moving the faces away from the origin the right amount, without changing the orientation or size of the faces, and patch the square holes in the result, you get a rhombicosidodecahedron.

The rhombicosidodecahedron shares the vertex arrangement with the small stellated truncated dodecahedron, and with the uniform compounds of six or twelve pentagrammic prisms.

The Zometool kits for making geodesic domes and other polyhedra use slotted balls as connectors.

Cartesian coordinates for the vertices of a rhombicosidodecahedron with an edge length of 2 centered at the origin are all even permutations of:[3] where φ = ⁠1 + √5/2⁠ is the golden ratio.

Therefore, the circumradius of this rhombicosidodecahedron is the common distance of these points from the origin, namely √φ6+2 = √8φ+7 for edge length 2.

This polyhedron is topologically related as a part of a sequence of cantellated polyhedra with vertex figure (3.4.n.4), which continues as tilings of the hyperbolic plane.