Dodecagonal-pentagonal antiprismatic duoprism

The dodecagonal-pentagonal antiprismatic duoprism or twapap is a convex uniform duoprism that consists of 12 pentagonal antiprismatic prisms, 2 pentagonal-dodecagonal duoprisms and 10 triangular-dodecagonal duoprisms. Each vertex joins 2 pentagonal antiprismatic prisms, 3 triangular-dodecagonal duoprisms, and 1 pentagonal-dodecagonal duoprism.

Vertex coordinates
The vertices of a dodecagonal-pentagonal antiprismatic duoprism of edge length 1 are given by all central inversions of the last three coordinates of:
 * $$\left(±\frac{1+\sqrt3}2,\,±\frac{1+\sqrt3}2,\,0,\,\sqrt{\frac{5+\sqrt5}{10}},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}2,\,0,\,\sqrt{\frac{5+\sqrt5}{10}},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(±\frac{2+\sqrt3}2,\,±\frac12,\,0,\,\sqrt{\frac{5+\sqrt5}{10}},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(±\frac{1+\sqrt3}2,\,±\frac{1+\sqrt3}2,\,±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}2,\,±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(±\frac{2+\sqrt3}2,\,±\frac12,\,±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(±\frac{1+\sqrt3}2,\,±\frac{1+\sqrt3}2,\,±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}2,\,±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(±\frac{2+\sqrt3}2,\,±\frac12,\,±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}},\,\sqrt{\frac{5+\sqrt5}{40}}\right).$$

Representations
A dodecagonal-pentagonal antiprismatic duoprism has the following Coxeter diagrams:
 * x12o s2s10o (full symmetry; pentagonal antiprisms as alternated decagonal prisms)
 * x12o s2s5s (pentagonal antiprisms as alternated dipentagonal prisms)
 * x6x s2s10o (dodecagons as dihexagons)
 * x6x s2s5s