Small ditrigonary icosidodecahedral prism

The small ditrigonary icosidodecahedral prism or sidtiddip, is a prismatic uniform polychoron that consists of 2 small ditrigonary icosidodecahedra, 12 pentagrammic prisms, and 20 triangular prisms. Each vertex joins 1 small ditrigonary icosidodecahedron, 3 pentagrammic prisms, and 3 triangular prisms. As the name suggests, it is a prism based on the small ditrigonary icosidodecahedron.

The small ditrigonary icosidodecahedral prism can be vertex-inscribed into the small stellated hecatonicosachoron.

Vertex coordinates
The vertices of a small ditrigonary icosidodecahedral prism of edge length 1 are given by all permutations and changes of sign of the first three coordinates of: along with all even permutations and all sign changes of:
 * $$\left(±\frac12,\,±\frac12,\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,0,\,±\frac12\right).$$

The first set of vertices are those of an inscribed tesseract, seen as a cubic prism.