Triangular-square antiprismatic duoprism

The triangular-square antiprismatic duoprism or trasquap is a convex uniform duoprism that consists of 3 square antiprismatic prisms, 2 triangular-square duoprisms, and 8 triangular duoprisms. Each vertex joins 2 square antiprismatic prisms, 3 triangular duoprisms, and 1 triangular-square duoprism. It is a duoprism based on a triangle and a square antiprism, which makes it a convex segmentoteron.

Vertex coordinates
The vertices of a triangular-square antiprismatic duoprism of edge length 1 are given by:
 * $$\left(0,\,\frac{\sqrt3}3,\,±\frac12,\,±\frac12,\,\frac{\sqrt[4]8}4\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}6,\,±\frac12,\,±\frac12,\,\frac{\sqrt[4]8}4\right),$$
 * $$\left(0,\,\frac{\sqrt3}3,\,0,\,±\frac{\sqrt2}2,\,-\frac{\sqrt[4]8}4\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}6,\,0,\,±\frac{\sqrt2}2,\,-\frac{\sqrt[4]8}4\right),$$
 * $$\left(0,\,\frac{\sqrt3}3,\,±\frac{\sqrt2}2,\,0,\,-\frac{\sqrt[4]8}4\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}6,\,±\frac{\sqrt2}2,\,0,\,-\frac{\sqrt[4]8}4\right).$$

Representations
A triangular-square antiprismatic duoprism has the following Coxeter diagrams:
 * x3o s2s8o (full symmetry; square antiprism as alternated octagonal prism)
 * x3o s2s4s (square antiprisms as alternated ditetragonal prisms)