Small ditrigonary icosidodecahedron

The small ditrigonal icosidodecahedron, or sidtid',' is a quasiregular uniform polyhedron. It consists of 20 equilateral triangles and 12 pentagrams, with three of each joining at a vertex.

Vertex coordinates
A small ditrigonal icosidodecahedron of side length 1 has vertex coordinates given by all permutations of and even permutations of
 * (±1/2, ±1/2, ±1/2),
 * (±(1+$\sqrt{5}$)/4, ±($\sqrt{3}$–1)/4, 0).

The first set of vertices correspond to those of an inscribed unit cube. tHis relates to the fact that a uniform compound of 5 cubes has the same vertices and edges as this polyhedron.

Related polyhedra
The small ditrigonal icosidodecahedron is the colonel of a three-member regiment that also includes the ditrigonal dodecadodecahedron and the great ditrigonal icosidodecahedron. This regiment also contains the rhombihedron, the uniform compound of 5 cubes.