Small Stellated Dodecahedron

The small stellated dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and one of the four nonconvex regular polyhedra. It is made of twelve pentagrammic faces, with five pentagrams meeting at each vertex, and it shares the same vertex arrangement as the convex regular icosahedron while sharing its edge arrangement with the great icosahedron, with which it forms a degenerate uniform compound figure. It is the second of the four stellations of the dodecahedron, counting the original dodecahedron itself as the first, and like the pentagram, its two dimensional analogue, it can be constructed by extending the edges of the core polytope until they intersect.