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. It is the first in an infinite family of isogonal decagonal hosohedral swirlchora and also the first in an infinite family of isochoric 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:


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