Great Stellated Dodecahedron

The great stellated dodecahedron is one of the four Kepler-Poinsot polyhedra, the non-convex regular star polyhedra, formed as a stellation of the regular dodecahedron with twelve intersecting pentagram faces meeting three at a vertex. It has twelve faces, thirty edges and twenty vertices, and is the dual of the great icosahedron. The German astronomer and mathematician Johannes Kepler first described it, together with the small stellated dodecahedron, in his 1619 work Harmonices Mundi, and in 1809 the French mathematician Louis Poinsot independently rediscovered both of Kepler's star polyhedra and identified the remaining two, the great dodecahedron and the great icosahedron, completing the set of four. Augustin-Louis Cauchy proved in 1811 that these four are the only regular star polyhedra that exist, a result later folded into the broader classification of regular polytopes.