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
Regular dodecahedron faces) is while the midradius, which touches the middle of each edge, is These quantities may also be expressed as where "ϕ" is the golden ratio. Note that, given a regular dodecahedron of edge length one, "r" is the radius of a circumscribing sphere about a cube of edge length "ϕ", and "r" is the apothem of a regular pentagon of edge length "ϕ". The surface area "A" and the volume "V" of a regular dodecahedron of edge length "a" are: Additionally, the surface area and volume of a regular dodecahedron are related to the golden ratio. A dodecahedron with