Hexagonal duotegum

The hexagonal duotegum or hiddit, also known as the hexagonal-hexagonal duotegum, the 6 duotegum, or the 6-6 duotegum, is a noble duotegum that consists of 36 tetragonal disphenoids and 12 vertices, with 12 cells joining at each vertex. It is also the 12-5 step prism. It is the first in an infinite family of isogonal hexagonal hosohedral swirlchora and also the first in an infinite family of isochoric hexagonal dihedral swirlchora.

The ratio between the longest and shortest edges is 1:$$\sqrt2$$ ≈ 1:1.41421.

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


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