Hexagonal-dodecagonal duoprismatic prism

The hexagonal-dodecagonal duoprismatic prism or hatwip, also known as the hexagonal-dodecagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 hexagonal-dodecagonal duoprisms, 6 square-dodecagonal duoprisms and 12 square-hexagonal duoprisms. Each vertex joins 2 square-hexagonal duoprisms, 2 square-dodecagonal duoprisms, and 1 hexagonal-dodecagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

This polyteron can be alternated into a triangular-hexagonal duoantiprismatic antiprism, although it cannot be made uniform. The dodecagons can also be alternated into long ditrigons to create a triangular-hexagonal prismatic prismantiprismoid, which is also nonuniform.

Vertex coordinates
The vertices of a hexagonal-dodecagonal duoprismatic prism of edge length 1 are given by all permutations of the third and fourth coordinates of:
 * $$\left(0,\,±1,\,±\frac{1+\sqrt3}2,\,±\frac{1+\sqrt3}2,\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt3}2,\,±\frac12,\,±\frac{1+\sqrt3}2,\,±\frac{1+\sqrt3}2,\,±\frac12\right),$$
 * $$\left(0,\,±1,\,±\frac12,\,±\frac{2+\sqrt3}2,\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt3}2,\,±\frac12,\,±\frac12,\,±\frac{2+\sqrt3}2,\,±\frac12\right).$$

Representations
A hexagonal-dodecagonal duoprismatic prism has the following Coxeter diagrams:
 * x x6o x12o (full symmetry)
 * x x3x x12o (hexagons as ditrigons)
 * x x6o x6x (dodecagons as dihexagons)
 * x x3x x6x
 * xx6oo xx12oo&#x (hexagonal-dodecagonal duoprism atop hexagonal-dodecagonal duoprism)
 * xx3xx xx12oo&#x
 * xx6oo xx6xx&#x
 * xx3xx xx6xx&#x