Square-pentagonal duoprism

The square-pentagonal duoprism or squipdip, also known as the 4-5 duoprism, is a uniform duoprism that consists of 4 pentagonal prisms and 5 cubes, with two of each joining at each vertex.

It is also a CRF segmentochoron, being a pentagonal prism atop pentagonal prism. It is designated K-4.42 on Richard Klitzing's list. It can thus be thought of as a prism based on the pentagonal prism.

Vertex coordinates
Coordinates for the vertices of a square-pentagonal duoprism with edge length 1 are given by:
 * $$\left(±\frac12,\,±\frac12,\,0,\,\sqrt{\frac{5+\sqrt5}{10}}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}}\right).$$

Representations
A suare-pentagonal duoprism has the following Coxeter diagrams:


 * x4o x5o (full symmetry)
 * x x x5o (H2×A1×A1 symmetry, square as rectangle)
 * xx xx5oo#x (H2×A1 axial, pentagonal prism prism)
 * ofx xxx4ooo&#xt (BC2×A1 axial, square-first)
 * ofx xxx xxx&#xt (A1×A1×A1, as above with rectangle symmetry)
 * oqo xxx5ooo&#xt (H2×A1 axial, pentagon-first)