Octagonal duoprismatic prism

The octagonal duoprismatic prism or oop, also known as the octagonal-octagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 octagonal duoprisms and 16 square-octagonal duoprisms. Each vertex joins 4 square-octagonal duoprisms and 1 octagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

The octagonal duoprismatic prism can be vertex-inscribed into a small prismated penteract.

This polyteron can be alternated into a square duoantiprismatic antiprism, although it cannot be made uniform. Half of the octagons can also be alternated into long rectangles to create a square-square prismatic prismantiprismoid, which is also nonuniform.

Vertex coordinates
The vertices of a octagonal duoprismatic prism of edge length 1 are given by:
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt2}2,\,±\frac12,\,±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac{1+\sqrt2}2,\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt2}2,\,±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac12,\,±\frac12\right),$$

Representations
An octagonal duoprismatic prism has the following Coxeter diagrams:
 * x x8o x8o (full symmetry)
 * x x4x x4x (octagons as ditetragons)
 * xx8oo xx8oo&#x (octagonal duoprism atop octagonal duoprism)
 * xx4xx xx4xx&#x