Decagonal duotegum

The decagonal duotegum or dedit, also known as the decagonal-decagonal duotegum, the 10 duotegum, or the 10-10 duotegum, is a noble duotegum that consists of 100 tetragonal disphenoids and 20 vertices, with 20 cells joining at each vertex. It is also the 20-9 step prism. Together with its dual, it is the fourth in an infinite family of square dihedral swirlchora and the first in an infinite family of decagonal dihedral swirlchora.

Vertex coordinates
The vertices of a decagonal duotegum based on 2 decagons of edge length 1, centered at the origin, are given by:


 * $$\left(±\frac12,\,±\frac{\sqrt{5+2\sqrt5}}{2},\,0,\,0\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\sqrt{\frac{5+\sqrt5}{8}},\,0,\,0\right),$$
 * $$\left(±\frac{1+\sqrt5}{2},\,0,\,0,\,0\right),$$
 * $$\left(0,\,0,\,±\frac12,\,±\frac{\sqrt{5+2\sqrt5}}{2}\right),$$
 * $$\left(0,\,0,\,±\frac{3+\sqrt5}{4},\,±\sqrt{\frac{5+\sqrt5}{8}}\right),$$
 * $$\left(0,\,0,\,±\frac{1+\sqrt5}{2},\,0\right).$$