Dodecagonal-icosahedral duoprism

The dodecagonal-icosahedral duoprism or twike is a convex uniform duoprism that consists of 12 icosahedral prisms and 20 triangular-dodecagonal duoprisms. Each vertex joins 2 icosahedral prisms and 5 triangular-dodecahedral duoprisms.

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

Representations
A dodecagonal-icosahedral duoprism has the following Coxeter diagrams:
 * x12o o5o3x (full symmetry)
 * x6x o5o3x (dodecagons as dihexagons)