Square-hexagonal duoprism

The square-hexagonal duoprism or shiddip, also known as the 4-6 duoprism, is a uniform duoprism that consists of 4 hexagonal prisms and 6 cubes, with two of each joining at each vertex.s.

It is also a CRF segmentochoron, being hexagonal prism atop hexagonal prism. It is designated K-4.54 on Richard Klitzing's list. As It can thus be thought of as a prism based on the hexagonal prism.

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

Vertex coordinates
The vertices of a square-hexagonal duoprism of edge length 1, centered at the origin, are given by:
 * $$\left(±\frac12,\,±\frac12,\,0,\,±1\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{\sqrt3}{2},\,±\frac12\right).$$

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


 * x4o x6o (full symmetry)
 * x x x6o (G2×A2×A2 symmetry, square as rectangle)
 * x3x x4o (A2×BC2 symmetry, hexagon as ditrigon)
 * x x x3x (A2×A1×A1 symmetry, both above combined
 * xx xx6oo&#x (G2×A1 axial, hexagonal prism prism)
 * xx xx3xx&#x (A2×A1 symmetry, as above with ditrigon symmetry)
 * xux xxx4ooo&#xt (BC2×A1 axial, cube-first)
 * xux xxx xxx&#xt (A1×A1×A1 axial, cube-first)
 * oqo xxx6ooo&#xt (G2×A1 axial, hexagon-first)
 * oqo xxx3xxx&#xt (A2×A1 axial, hexagon-first)