Snub dodecahedral prism

The snub dodecahedral prism or sniddip is a prismatic uniform polychoron that consists of 2 snub dodecahedra, 12 pentagonal prisms, and 20+60 triangular prisms. Each vertex joins 1 snub dodecahedron, 1 pentagonal prism, and 4 triangular prisms. It is a prism based on the snub dodecahedron. As such it is also a convex segmentochoron (designated K-4.110 on Richard Klitzing's list).

Vertex coordinates
The coordinates of a snub dodecahedral prism, centered at the origin and with unit edge length, are given by all even permutations with an odd number of sign changes of the first three coordinates of: as well as all even permutations with an even number of sign changes of the first three coordinates of: where
 * $$\left(\frac{\phi\sqrt{\phi(\xi-1-\frac1\xi)}}2,\,\frac{\xi\phi\sqrt{3-\xi^2}}2,\,\frac{\phi\sqrt{\xi(\xi+\phi)+1}}2,\,±\frac12\right),$$
 * $$\left(\frac{\phi\sqrt{3-\xi^2}}2,\,\frac{\xi\phi\sqrt{1-\xi+\frac{1+\phi}\xi}}2,\,\frac{\phi\sqrt{\xi(\xi+1)}}2,\,±\frac12\right),$$
 * $$\left(\frac{\xi^2\phi\sqrt{\phi(\xi-1-\frac1\xi)}}2,\,\frac{\phi\sqrt{\xi+1-\phi}}2,\,\frac{\sqrt{\xi^2(1+2\phi)-\phi}}2,\,±\frac12\right),$$
 * $$\left(\frac{\xi^2\phi\sqrt{3-\xi^2}}2,\,\frac{\xi\phi\sqrt{\phi(\xi-1-\frac1\xi)}}2,\,\frac{\phi^2\sqrt{\xi(\xi+\phi)+1}}{2\xi},\,±\frac12\right),$$
 * $$\left(\frac{\sqrt{\phi(\xi+2)+2}}2,\,\frac{\phi\sqrt{1-\xi+\frac{1+\phi}\xi}}2,\,\frac{\xi\sqrt{\xi(1+\phi)-\phi}}2,\,±\frac12\right),$$
 * $$\phi = \frac{1+\sqrt5}2,$$
 * $$\xi = \sqrt[3]{\frac{\phi+\sqrt{\phi-\frac5{27}}}2}+\sqrt[3]{\frac{\phi-\sqrt{\phi-\frac5{27}}}2}.$$