Great stellated dodecahedron

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Great stellated dodecahedron
Great stellated dodecahedron.png
Type Kepler-Poinsot polyhedron
Stellation core dodecahedron
Elements F = 12, E = 30
V = 20 (χ = 2)
Faces by sides 12{5/2}
Schläfli symbol {5/2,3}
Wythoff symbol 3 | 25/2
Coxeter-Dynkin CDel node.pngCDel 3.pngCDel node.pngCDel 5.pngCDel rat.pngCDel d2.pngCDel node 1.png
Symmetry group Ih, H3, [5,3], (*532)
References U52, C68, W22
Properties Regular nonconvex
Great stellated dodecahedron vertfig.png
(5/2)3
(Vertex figure)
Great icosahedron.png
Great icosahedron
(dual polyhedron)

In geometry, the great stellated dodecahedron is a Kepler-Poinsot polyhedron, with Schläfli symbol {5/2,3}. It is one of four nonconvex regular polyhedra.

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.

If the pentagrammic faces are broken into triangles, it is topologically related to the triakis icosahedron, with the same face connectivity, but much taller isosceles triangle faces.

Images[edit]

Transparent model Tiling
GreatStellatedDodecahedron.jpg
Transparent great stellated dodecahedron (Animation)
Great stellated dodecahedron tiling.png
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)
Net Stellation facets
Third stellation of dodecahderon net.svg
A net of a great stellated dodecahedron
Third stellation of dodecahedron facets.svg
It can be constructed as the third of three stellations of the dodecahedron, and referenced as Wenninger model [W22].

Related polyhedra[edit]

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.

Name Great
stellated
dodecahedron
Truncated great stellated dodecahedron Great
icosidodecahedron
Truncated
great
icosahedron
Great
icosahedron
Coxeter-Dynkin
diagram
CDel node.pngCDel 3.pngCDel node.pngCDel 5.pngCDel rat.pngCDel d2.pngCDel node 1.png CDel node.pngCDel 3.pngCDel node 1.pngCDel 5.pngCDel rat.pngCDel d2.pngCDel node 1.png CDel node.pngCDel 3.pngCDel node 1.pngCDel 5.pngCDel rat.pngCDel d2.pngCDel node.png CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 5.pngCDel rat.pngCDel d2.pngCDel node.png CDel node 1.pngCDel 3.pngCDel node.pngCDel 5.pngCDel rat.pngCDel d2.pngCDel node.png
Picture Great stellated dodecahedron.png Icosahedron.png Great icosidodecahedron.png Great truncated icosahedron.png Great icosahedron.png

References[edit]

External links[edit]

Stellations of the dodecahedron
Platonic solid Kepler-Poinsot solids
Dodecahedron Small stellated dodecahedron Great dodecahedron Great stellated dodecahedron
Zeroth stellation of dodecahedron.png First stellation of dodecahedron.svg Second stellation of dodecahedron.png Third stellation of dodecahedron.png
Zeroth stellation of dodecahedron facets.png First stellation of dodecahedron facets.png Second stellation of dodecahedron facets.png Third stellation of dodecahedron facets.png