Octagonal-cubic duoprism

The octagonal-cubic duoprism or ocube, also known as a square-octagonal duoprismatic prism, is a convex uniform duoprism that consists of 8 tesseracts and 6 square-octagonal duoprisms. Each vertex joins 2 tesseracts and 3 square-octagonal duoprisms. It is a duoprism based on a square and an octagonal prism, which makes it a convex segmentoteron.

This polyteron can be alternated into a square-tetrahedral duoantiprism, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create a tetrahedral-square prismantiprismoid, which is also nonuniform.

It can be vertex-inscribed into the small cellated penteractitriacontaditeron.

Vertex coordinates
The vertices of an octagonal-cubic duoprism of edge length 1 are given by:
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac12\right).$$

Representations
An octagonal-cubic duoprism has the following Coxeter diagrams:
 * x8o x4o3o (full symmetry)
 * x4x x4o3o (octagons as ditetragons)
 * x x4o x8o (square-octagonal duoprismatic prism)
 * x x4o x4x
 * x x x x8o (octagonal prismatic prismatic prism)
 * x x x x4x