Small stellated dodecahedron

The small stellated dodecahedron, or sissid, is one of the four Kepler–Poinsot solids. It has 12 pentagrams as faces, joining 5 to a vertex.

It is the first stellation of a dodecahedron, from which its name is derived.

Vertex coordinates
The vertices of a small stellated dodecahedron of edge length 1, centered at the origin, are all cyclic permutations of


 * (0, ±1/2, ±($\sqrt{5}$–1)/4).

Related polyhedra
The small stellated dodecahedron is the colonel of a two-member regiment that also includes the great icosahedron.