Icosidodecahedral prism

The icosidodecahedral prism or iddip, is a prismatic uniform polychoron that consists of 2 icosidodecahedra, 12 pentagonal prisms, and 20 triangular prisms. Each vertex joins 1 icosidodecahedron, 2 pentagonal prisms, and 2 triangular prisms. As the name suggests, it is a prism based on the icosidodecahedron. As such it is also a convex segmentochoron (designated K-4.90 on Richard Klitzing's list).

Vertex coordinates
The vertices of an icosidodecahedral prism of edge length 1 are given by all permutations and sign changes of the first three coordinates of: along with all even permutations and all sign changes of the first three coordinates of:
 * $$\left(0,\,0,\,±\frac{1+\sqrt5}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac12\right).$$

Representations
An icosidodecahedral prism has the following Coxeter diagrams:


 * x o5x3o (full symmetry)
 * oo5xx3oo&#x (bases seen separately)
 * xxxxx xoxfo5ofxox&#xt (H2×A1 axial, pentagonal prism-first)

Related polychora
The regiment of the icosidodecahedral prism also includes the small icosihemidodecahedral prism and small dodecahemidodecahedral prism.