Great dodecahedron

Great dodecahedron

In geometry, the great dodecahedron is a Kepler-Poinsot polyhedron. 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.

Features

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

This shape was the basis for the Rubik's Cube-like Alexander's Star puzzle.

It is considered the second of three stellations of the dodecahedron.

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.

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As a stellation

It can also be constructed as the second of four stellations of the dodecahedron, and referenced as [List of Wenninger polyhedron models#Stellations of dodecahedron|Wenninger model [W21] .

The stellation facets for construction are::

Net

A great dodecahedron has a net like the following:

Fold forward on the short lines, and backwards on the long lines.

External links

*
** mathworld | urlname = DodecahedronStellations| title =Three dodecahedron stellations
* [http://bulatov.org/metal/dodecahedron_7.html Metal sculpture of Great Dodecahedron]


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