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:
 * (0, 0, ±(1+$\sqrt{5}$)/2, ±1/2),
 * (±1/2, ±(1+$\sqrt{2}$)/4, ±(3+$\sqrt{7+2√5}$)/4, ±1/2).

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)