Octagonal-square antiprismatic duoprism

The octagonal-square antiprismatic duoprism or osquap is a convex uniform duoprism that consists of 8 square antiprismatic prisms, 2 square-octagonal duoprisms and 8 triangular-octagonal duoprisms. Each vertex joins 2 square antiprismatic prisms, 3 triangular-octagonal duoprisms, and 1 square-octagonal duoprism.

Vertex coordinates
The vertices of an octagonal-square antiprismatic duoprism of edge length 1 are given by all permutations of the first two coordinates of:
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac12,\,±\frac12,\,\frac{\sqrt[4]8}4\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,0,\,±\frac{\sqrt2}2,\,-\frac{\sqrt[4]8}4\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,±\frac{\sqrt2}2,\,0,\,-\frac{\sqrt[4]8}4\right).$$

Representations
An octagonal-square antiprismatic duoprism has the following Coxeter diagrams:
 * x8o s2s8o (full symmetry; square antiprisms as alternated octagonal prisms)
 * x8o s2s4s (square antiprisms as alternated ditetragonal prisms)
 * x4x s2s8o (octagons as ditetragons)
 * x4x s2s4s