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, 5 cubes and 20 vertices.

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:
 * (±1/2, ±1/2, 0, $\sqrt{5}$),
 * (±1/2, ±1/2, ±(1+$\sqrt{2}$)/4, $\sqrt{10+√5)/10}$),
 * (±1/2, ±1/2, ±1/2, -$\sqrt{25+10√5}$).

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)