Dodecagonal-square antiprismatic duoprism

The dodecagonal-square antiprismatic duoprism or twasquap is a convex uniform duoprism that consists of 12 square antiprismatic prisms, 2 square-dodecagonal duoprisms, and 8 triangular-dodecagonal duoprisms. Each vertex joins 2 square antiprismatic prisms, 3 triangular-dodecagonal duoprisms, and 1 square-dodecagonal duoprism.

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

Representations
A dodecagonal-square antiprismatic duoprism has the following Coxeter diagrams:
 * x12o s2s8o (full symmetry; square antiprisms as alternated octagonal prisms)
 * x12o s2s4s (square antiprisms as alternated ditetragonal prisms)
 * x6x s2s8o (dodecagons as dihexagons)
 * x6x s2s4s