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


 * $$\left(0,\,±\frac{1}{2},\,±\frac{\sqrt{5}-1}{4}\right).$$

In vertex figures
The small stellated dodecahedron appears as a vertex figure of two Schläfli–Hess polychora.

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

Two uniform polyhedron compounds are composed of small stellated dodecahedra:


 * Pentagrammatic snub pseudodisoctahedron (2)
 * Pentagrammatic snub pseudicosicosahedron (5)