Monday, October 22, 2012

Kepler–Poinsot polyhedra

In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra. They may be obtained by stellating the regular convex dodecahedron and icosahedron, and differ from these in having regular pentagrammic faces or vertex figures.

The four Kepler–Poinsot polyhedra are illustrated above. Each is identified by its Schläfli symbol, of the form {p, q}, and by its name. One face of each figure is shown yellow and outlined in red.

Great Dodecahedron
Small Stelated Dodecahedron

Great Icosahedron

Great Dodecahedron

Great Stellated Dodecahedron

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