Great stellated dodecahedron of uniform polyhedra. Truncating edges down to points produces the great icosidodecahedron as a rectified great stellated dodecahedron. The process completes as a birectification, reducing the original faces down to points, and producing the great icosahedron. The truncated "great stellated dodecahedron" is a degenerate polyhedron, with 20 triangular faces from the truncated vertices, and 12 (hidden) pentagonal faces as truncations of the original pentagram faces, the latter forming a great dodecahedron inscribed within and sharing the edges of the icosahedron. Great stellated dodecahedron In geometry, the great stellated dodecahedron is a Kepler-Poinsot polyhedron, with Schläfli symbol {5/2,3}. It is one
Small stellated dodecahedron the form of doubly-wound pentagons overlapping the first 12 pentagons. The latter faces are formed by truncating the original pentagrams. When an {n/d}-gon is truncated, it becomes a {2n/d}-gon. For example, a truncated pentagon {5/1} becomes a decagon {10/1}, so truncating a pentagram {5/2} becomes a doubly-wound pentagon {10/2} (the common factor between 10 and 2 mean we visit each vertex twice to complete the polygon). Small stellated dodecahedron In geometry, the small stellated dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol {5/2,5}. It is one of four nonconvex regular polyhedra. It is composed of