Dodecagonal-great rhombicuboctahedral duoprism

The dodecagonal-great rhombicuboctahedral duoprism or twagirco is a convex uniform duoprism that consists of 12 great rhombicuboctahedral prisms, 6 octagonal-dodecagonal duoprisms, 8 hexagonal-dodecagonal duoprisms, and 12 square-dodecagonal duoprisms. Each vertex joins 2 great rhombicuboctahedral prisms, 1 square-dodecagonal duoprism, 1 hexagonal-dodecagonal duoprism, and 1 octagonal-dodecagonal duoprism.

This polyteron can be alternated into a hexagonal-snub cubic duoantiprism, although it cannot be made uniform. The dodecagons can also be edge-snubbed to create a snub cubic-hexagonal prismantiprismoid or the great rhombicuboctahedra to create a hexagonal-pyritohedral prismantiprismoid, which are also both nonuniform.

Vertex coordinates
The vertices of a dodecagonal-great rhombicuboctahedral duoprism of edge length 1 are given by all permutations of the last three coordinates of:
 * $$\left(±\frac{1+\sqrt3}2,\,±\frac{1+\sqrt3}2,\,±\frac{1+2\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}2,\,±\frac{1+2\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac12\right),$$
 * $$\left(±\frac{2+\sqrt3}2,\,±\frac12,\,±\frac{1+2\sqrt2}{2},\,±\frac{1+\sqrt2}{2},\,±\frac12\right).$$

Representations
A dodecagonal-great rhombicuboctahedral duoprism has the following Coxeter diagrams:
 * x12o x4x3x (full symmetry)
 * x6x x4x3x (dodecagons as dihexagons)