Great stellated dodecahedron
In geometry, the great stellated dodecahedron is a Kepler–Poinsot polyhedron, with Schläfli symbol,3
Images
| Transparent model | Tiling |
Transparent great stellated dodecahedron | This polyhedron can be made as spherical tiling with a density of 7. |
| Net | Stellation facets |
A net of a great stellated dodecahedron ; twenty isosceles triangular pyramids, arranged like the faces of an icosahedron. | It can be constructed as the third of three stellations of the dodecahedron, and referenced as List of Wenninger polyhedron models#Stellations of dodecahedron|Wenninger model . |
Complete net of the surface geometry of a great stellated dodecahedron. Making a net with the actual pentagrams that make up the polyhedron would self intersect even if layed out flat. | - |
Formulas
For a great stellated dodecahedron with edge length E,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 pentagonal faces as truncations of the original pentagram faces, the latter forming a great dodecahedron inscribed within and sharing the edges of the icosahedron.
| Name | Great stellated dodecahedron | Truncated great stellated dodecahedron | Great icosidodecahedron | Truncated great icosahedron | Great icosahedron |
| Coxeter-Dynkin diagram | |||||
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