Rectified hexagonal duoprism

The rectified hexagonal duoprism or rehiddip is a convex isogonal polychoron that consists of 12 rectified hexagonal prisms and 36 tetragonal disphenoids. 3 rectified hexagonal prisms and 2 tetragonal disphenoids join at each vertex. It can be formed by rectifying the hexagonal duoprism.

It can also be formed as the convex hull of 2 oppositely oriented semi-uniform hexagonal duoprisms, where the edges of one hexagon are $$\frac{2\sqrt3}{3} ≈ 1.15470$$ as long as the edges of the other.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt6}{2}$$ ≈ 1:1.22474.

Vertex coordinates
The vertices of a rectified hexagonal duoprism based on hexagons of edge length 1, centered at the origin, are given by:


 * $$\left(0,\,±1,\,0,\,±\frac{2\sqrt3}{3}\right),$$
 * $$\left(0,\,±1,\,±1,\,±\frac{\sqrt3}{3}\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,0,\,±\frac{2\sqrt3}{3}\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,±1,\,±\frac{\sqrt3}{3}\right),$$
 * $$\left(±\frac{2\sqrt3}{3},\,0,\,±1,\,0\right),$$
 * $$\left(±\frac{2\sqrt3}{3},\,0,\,±\frac12,\,±\frac{\sqrt3}{2}\right),$$
 * $$\left(±\frac{\sqrt3}{3},\,±1,\,±1,\,0\right),$$
 * $$\left(±\frac{\sqrt3}{3},\,±1,\,±\frac12,\,±\frac{\sqrt3}{2}\right).$$