Hexagonal duoprism

The hexagonal duoprism or hiddip, also known as the hexagonal-hexagonal duoprism, the 6 duoprism or the 6-6 duoprism, is a noble uniform duoprism that consists of 12 hexagonal prisms, with 4 joining at each vertex. It is also the 12-5 gyrochoron. It is the first in an infinite family of isogonal hexagonal dihedral swirlchora and also the first in an infinite family of isochoric hexagonal hosohedral swirlchora.

This polychoron can be alternated into a triangular duoantiprism, although it cannot be made uniform.

A unit hexagonal duoprism can be vertex-inscribed into the antifrustary distetracontoctachoron and ditetrahedronary dishecatonicosachoron.

Vertex coordinates
Coordinates for the vertices of a hexagonal duoprism of edge length 1, centered at the origin, are given by:
 * $$\left(0,\,±1,\,0,\,±1\right),$$
 * $$\left(0,\,±1,\,±\frac{\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,0,\,±1\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,±\frac{\sqrt3}{2},\,±\frac12\right).$$

Representations
A hexagonal duoprism has the following Coxeter diagrams:


 * x6o x6o (full symmetry)
 * x3x x6o (one hexagon seen as ditrigon)
 * x3x x3x (both hexagons seen as ditrigons, triangular duoprismatic symmetry)
 * xux xxx6ooo&#xt (hexagonal axial)
 * xux xxx3xxx&#xt (ditrigonal axial)