Small ditrigonary icosidodecahedron

The small ditrigonary 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.

It can be constructed as a holosnub dodecahedron.

This polyhedron is the vertex figure of the small ditrigonary hexacosihecatonicosachoron.

Vertex coordinates
A small ditrigonary icosidodecahedron of side length 1 has vertex coordinates given by all permutations of and even permutations of
 * $$\left(±\frac12,\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,0\right).$$

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.

Representations
A small ditrigonary icosidodecahedron has the following Coxeter diagrams:


 * x5/2o3o3*a
 * ß5o3o (as holosnub)

Related polyhedra
The small ditrigonary icosidodecahedron is the colonel of a three-member regiment that also includes the ditrigonary dodecadodecahedron and the great ditrigonary icosidodecahedron. This regiment also contains the rhombihedron, the uniform compound of 5 cubes. The pentagrammic cuploid and pentagonal cuploid are contained within the edge structure.