Hexagonal-cubic duoprism

The hexagonal-cubic duoprism or hacube, also known as a square-hexagonal duoprismatic prism, is a convex uniform duoprism that consists of 6 tesseracts and 6 square-hexagonal duoprisms. Each vertex joins 2 tesseracts and 3 square-hexagonal duoprisms. It is a duoprism based on a square and a hexagonal prism, which makes it a convex segmentoteron.

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

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

Representations
A hexagonal-cubic duoprism has the following Coxeter diagrams:
 * x6o x4o3o (full symmetry)
 * x3x x4o3o (hexagons as ditrigons)
 * x x4o x6o (square-hexagonal duoprismatic prism)
 * x x3x x4o
 * x x x x6o (hexagonal prismatic prismatic prism)
 * x x x x3x
 * xx4oo xx6oo&#x (square-hexagonal duoprism atop square-hexagonal duoprism)
 * xx xx xx6oo&#x
 * xx4oo xx3xx&#x
 * xx xx xx3xx&#x