Pentagonal-pentagrammic duotegum

The pentagonal-pentagrammic duotegum, also known as the 5-5/2 duotegum, is a duotegum that consists of 25 regular tetrahedra and 10 vertices.

This is one of only two 4D duotegums that can be made to have regular tetrahedral cells and equilateral triangular faces. The other is the square duotegum, which is the regular hexadecachoron.

Vertex coordinates
The vertices of a pentagonal-pentagrammic duotegum of edge length 1 are given by:


 * $$\left(±\frac{1}{2},\, -\sqrt{\frac{5+2\sqrt{5}}{20}},\,0,\,0\right),$$
 * $$\left(±\frac{1+\sqrt{5}}{4},\, \sqrt{\frac{5-\sqrt{5}}{40}},\,0,\,0\right),$$
 * $$\left(0,\, \sqrt{\frac{5+\sqrt{5}}{10}},\,0,\,0\right),$$
 * $$\left(0,\,0,\,±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}}\right),$$
 * $$\left(0,\,0,\,±\frac{\sqrt5-1}{4},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(0,\,0,\,0,\,-\sqrt{\frac{5-\sqrt5}{10}}\right).$$