Great dodecahedron

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Great dodecahedron
Great dodecahedron.png
Type Kepler-Poinsot polyhedron
Stellation core dodecahedron
Elements F = 12, E = 30
V = 12 (χ = -6)
Faces by sides 12{5}
Schläfli symbol {5,5/2}
Wythoff symbol 5/2 | 2 5
Coxeter-Dynkin CDel node 1.pngCDel 5.pngCDel node.pngCDel 5.pngCDel rat.pngCDel d2.pngCDel node.png
Symmetry group Ih, H3, [5,3], (*532)
References U35, C44, W21
Properties Regular nonconvex
Great dodecahedron vertfig.png
(55)/2
(Vertex figure)
Small stellated dodecahedron.png
Small stellated dodecahedron
(dual polyhedron)

In geometry, the great dodecahedron is a Kepler-Poinsot polyhedron, with Schläfli symbol {5,5/2} and Coxeter-Dynkin diagram of CDel node 1.pngCDel 5.pngCDel node.pngCDel 5.pngCDel rat.pngCDel d2.pngCDel node.png. It is one of four nonconvex regular polyhedra. It is composed of 12 pentagonal faces (six pairs of parallel pentagons), with five pentagons meeting at each vertex, intersecting each other making a pentagrammic path.

Images[edit]

Transparent model Spherical tiling
GreatDodecahedron.jpg
(With animation)
Great dodecahedron tiling.png
This polyhedron represents a spherical tiling with a density of 3. (One spherical pentagon face is shown above in yellow)
Net Stellation
Second stellation of dodecahderon net.svg
Net for surface geometry
Second stellation of dodecahedron facets.svg
It can also be constructed as the second of three stellations of the dodecahedron, and referenced as Wenninger model [W21].

Related polyhedra[edit]

It shares the same edge arrangement as the convex regular icosahedron.

If the great dodecahedron is considered as a properly intersected surface geometry, it has the same topology as a triakis icosahedron with concave pyramids rather than convex ones.

A truncation process applied to the great dodecahedron produces a series of nonconvex uniform polyhedra. Truncating edges down to points produces the dodecadodecahedron as a rectified great dodecahedron. The process completes as a birectification, reducing the original faces down to points, and producing the small stellated dodecahedron.

Name Small stellated dodecahedron Dodecadodecahedron Truncated
great
dodecahedron
Great
dodecahedron
Coxeter-Dynkin
diagram
CDel node.pngCDel 5.pngCDel node.pngCDel 5.pngCDel rat.pngCDel d2.pngCDel node 1.png CDel node.pngCDel 5.pngCDel node 1.pngCDel 5.pngCDel rat.pngCDel d2.pngCDel node.png CDel node 1.pngCDel 5.pngCDel node 1.pngCDel 5.pngCDel rat.pngCDel d2.pngCDel node.png CDel node 1.pngCDel 5.pngCDel node.pngCDel 5.pngCDel rat.pngCDel d2.pngCDel node.png
Picture Small stellated dodecahedron.png Dodecadodecahedron.png Great truncated dodecahedron.png Great dodecahedron.png

Usage[edit]

See also[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