Great stellated dodecahedron
|Great stellated dodecahedron|
|Stellation core||regular dodecahedron|
|Elements||F = 12, E = 30
V = 20 (χ = 2)
|Faces by sides||125|
|Wythoff symbol||3 | 25/|
|Symmetry group||Ih, H3, [5,3], (*532)|
|References||U52, C68, W22|
It is composed of 12 intersecting pentagrammic faces, with three pentagrams meeting at each vertex.
It shares its vertex arrangement with the regular dodecahedron, as well as being a stellation of a (smaller) dodecahedron. It is the only dodecahedral stellation with this property, apart from the dodecahedron itself. Its dual, the great icosahedron, is related in a similar fashion to the icosahedron.
Shaving the triangular pyramids off results in an icosahedron.
Transparent great stellated dodecahedron (Animation)
This polyhedron can be made as spherical tiling with a density of 7. (One spherical pentagram face is shown above, outlined in blue, filled in yellow)
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A net of a great stellated dodecahedron (surface geometry); 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 Wenninger model [W22].
Complete net of a great stellated dodecahedron.
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.
|Truncated great stellated dodecahedron||Great
- Eric W. Weisstein, Great stellated dodecahedron (Uniform polyhedron) at MathWorld.
|Stellations of the dodecahedron|
|Platonic solid||Kepler–Poinsot solids|
|Dodecahedron||Small stellated dodecahedron||Great dodecahedron||Great stellated dodecahedron|