Octagonal duotegum

The octagonal duotegum or odit, also known as the octagonal-octagonal duotegum, the 8 duotegum, or the 8-8 duotegum, is a noble duotegum that consists of 64 tetragonal disphenoids and 16 vertices, with 16 cells joining at each vertex. It is also the digonal double gyroantiprismoid and the 16-7 step prism. It is the first in an infinite family of isogonal octagonal hosohedral swirlchora.

It is one of a number of isogonal polychora that can be obtained as the hull of various arrangements of 2 hexadecachora.

Vertex coordinates
The vertices of an octagonal duotegum based on 2 octagons of edge length 1, centered at the origin, are given by:


 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,0,\,0\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}{2},\,0,\,0\right),$$
 * $$\left(0,\,0,\,±\frac{1+\sqrt2}{2},\,±\frac12\right),$$
 * $$\left(0,\,0,\,±\frac12,\,±\frac{1+\sqrt2}{2}\right).$$