Icosidodecahedron

[…]together to form not only regular polyhedrons but rhombicosidodecahedrons, truncated icosidodecahedrons, and such.

1992, Jean-Louis Verger-Gaugry, Quasicrystals and the Concept of Interpenetration in m35-approximant Crystals with Long-range Icosahedral Atomic Clustering, A. R. Yavari, Ordering and Disordering in Alloys, Elsevier Applied Science, page 498, A succession of 10 concentric icosidodecahedra centered at (0, 0, 0), forming a geometric sequence (the nᵗʰ one is τⁿ larger than the first one), is also put into evidence.

The edges of the octahedron form three squares; the edges of the cuboctahedron form four hexagons, and the edges of the icosidodecahedron form six decagons.

Thus, there is a star octahedron, three star dodecahedrons, and fifty-nine star icosidodecahedrons.

The dark-gray (online: red) icosahedra are part of the B clusters, the light-gray dodecahedra of the B’ clusters, and the (online: blue) icosidodecahedra of the M clusters.

Polyhedrons include prisms; pyramids; the Platonic solids, including tetrahedrons, cubes, octahedrons, dodecahedrons, and icosahedrons; the Archimedean solids, such as cuboctahedrons and icosidodecahedrons; and the Johnson solids, such as square pyramids and triangular cupolas (dome-shape).