Dodecagonal-small rhombicosidodecahedral duoprism

The dodecagonal-small rhombicosidodecahedral duoprism or twasrid is a convex uniform duoprism that consists of 12 small rhombicosidodecahedral prisms, 12 pentagonal-dodecagonal duoprisms, 30 square-dodecagonal duoprisms, and 20 triangular-dodecagonal duoprisms. Each vertex joins 2 small rhombicosidodecahedral prisms, 1 triangular-dodecagonal duoprism, 2 square-dodecagonal duoprisms, and 1 pentagonal-dodecagonal duoprism.

Vertex coordinates
The vertices of a dodecagonal-small rhombicosidodecahedral duoprism of edge length 1 are given by all permutations of the last three coordinates of: as well as all even permutations of the last three coordinates of:
 * $$\left(±\frac{1+\sqrt3}2,\,±\frac{1+\sqrt3}2,\,±\frac12,\,±\frac12,\,±\frac{2+\sqrt5}2\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}2,\,±\frac12,\,±\frac12,\,±\frac{2+\sqrt5}2\right),$$
 * $$\left(±\frac{2+\sqrt3}2,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac{2+\sqrt5}2\right),$$
 * $$\left(±\frac{1+\sqrt3}2,\,±\frac{1+\sqrt3}2,\,0,\,±\frac{3+\sqrt5}4,\,±\frac{5+\sqrt5}4\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}2,\,0,\,±\frac{3+\sqrt5}4,\,±\frac{5+\sqrt5}4\right),$$
 * $$\left(±\frac{2+\sqrt3}2,\,±\frac12,\,0,\,±\frac{3+\sqrt5}4,\,±\frac{5+\sqrt5}4\right),$$
 * $$\left(±\frac{1+\sqrt3}2,\,±\frac{1+\sqrt3}2,\,±\frac{1+\sqrt5}4,\,±\frac{1+\sqrt5}2,\,±\frac{3+\sqrt5}4\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}2,\,±\frac{1+\sqrt5}4,\,±\frac{1+\sqrt5}2,\,±\frac{3+\sqrt5}4\right),$$
 * $$\left(±\frac{2+\sqrt3}2,\,±\frac12,\,±\frac{1+\sqrt5}4,\,±\frac{1+\sqrt5}2,\,±\frac{3+\sqrt5}4\right).$$

Representations
A dodecagonal-small rhombicosidodecahedral duoprism has the following Coxeter diagrams:
 * x12o x5o3x (full symmetry)
 * x6x x5o3x (dodecagons as dihexagons)