Rhombic Triacontahedra

Extract

The process of producing the facial planes of a polyhedron to form stellated polyhedra is well known. When applied to the icosahedron it leads to a series which is limited to eight solids if we make the condition that every face of each must be covered in forming the next of the series. If this condition is dropped a large number of combinations of the parts of these eight solids is possible. The total number of solids, limited by symmetry considerations, is 59, and they are all illustrated in The 59 Icosahedra by Coxeter, Du Val, Flather, and Petrie. The corresponding basic series of solids starting with the Rhombic Triacontahedron numbers 13, and the total number of combinations is very great.