Great stellated dodecahedron
- Great stellated dodecahedron
In geometry, the great stellated dodecahedron is a Kepler-Poinsot polyhedron. 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.
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As a stellation
It can also be constructed as the third of three stellations of the dodecahedron, and referenced as [List of Wenninger polyhedron models#Stellations of dodecahedron|Wenninger model [W22] .
The stellation facets for construction are::
Net
The net of a great stellated dodecahedron looks somewhat like this:
Fold forward on the short lines, and backwards on the long lines.
References
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External links
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** mathworld | urlname = DodecahedronStellations| title = Three stellations of the dodecahedron
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