Pentagonal duotegum

The pentagonal duotegum or pedit, also known as the pentagonal-pentagonal duotegum, the 5 duotegum, or the 5-5 duotegum, is a noble duotegum that consists of 25 tetragonal disphenoids and 10 vertices, with 10 cells joining at each vertex. It is also the 10-4 step prism and the square funk tegum. Together with its dual, it is the first in an infinite family of pentagonal dihedral swirlchora.

Vertecx coordinates
The vertices of a pentagonal duotegum based on two pentagons of edge length 1, centered at the origin, are given by:


 * $$\left(±\frac{1}{2},\, -\sqrt{\frac{5+2\sqrt{5}}{20}},\,0,\,0\right),$$
 * $$\left(±\frac{1+\sqrt{5}}{4},\, \sqrt{\frac{5-\sqrt{5}}{40}},\,0,\,0\right),$$
 * $$\left(0,\, \sqrt{\frac{5+\sqrt{5}}{10}},\,0,\,0\right),$$
 * $$\left(0,\,0,\,±\frac{1}{2},\, -\sqrt{\frac{5+2\sqrt{5}}{20}}\right),$$
 * $$\left(0,\,0,\,±\frac{1+\sqrt{5}}{4},\, \sqrt{\frac{5-\sqrt{5}}{40}}\right),$$
 * $$\left(0,\,0,\,0,\, \sqrt{\frac{5+\sqrt{5}}{10}}\right).$$