Square-decagonal duoprism

The square-decagonal duoprism or squadedip, also known as the 4-10 duoprism, is a uniform duoprism that consists of 4 decagonal prisms and 10 cubes, with two of each joining at each vertex.

It is a prism based on the decagonal prism. As such it is also a CRF segmentochoron, designated K-4.97 on Richard Klitzing's list.

This polychoron can be alternated into a digonal-pentagonal duoantiprism, although it cannot be made uniform.

Vertex coordinates
Coordinates for the vertices of a square-decagonal duoprism with edge length 1 are given by:
 * $$\left(±\frac12,\,±\frac12,\,0,\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12\right).$$

Representations
A square-decagonal duoprism has the following Coxeter diagrams:


 * x4o x10o (full symmetry)
 * x4o x5x (BC2×H2 symmetry, decagon as dipetnagon)
 * x x x10o (I2(10)×A1×A1 symmetry, square as rectangle)
 * x x x5x (H2×A1×A1 symmetry, both above)
 * xx xx10oo (I2(10)×A1 symmetry, decagon prismatic prism)
 * xx xx5xx&#x (H2×A1 axial, as above)
 * oqo xxx10ooo&#xt
 * oqo xxx5xxx&#xt (H2×A1 axial, decagon-first)