Great stellated dodecahedron

For a great stellated dodecahedron with edge length E (where E represents the length of any edge of the internal icosahedron), \text{Inradius} = {\tfrac{\text{E}(\sqrt{5}-1)}{2}} \text{Midradius} = {\tfrac{\text{E}(1+\sqrt{5})}{4}} \text{Circumradius} = {\tfrac{\text{E}(3+\sqrt{5})\sqrt{3}}{4}} \text{Surface Area} = 15\sqrt{5+2\sqrt{5}}\text{E}^2 \text{Volume} = {\tfrac{5(3+\sqrt{5})\text{E}^3}{4}} ==Related polyhedra==

A truncation process applied to the great stellated dodecahedron produces a series 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. == References ==