Pentagrammic disphenoid

The pentagrammic disphenoid, or stadow, is a noble scaliform polyteron with 10 pentagrammic scalenes and 10 vertices. 7 facets join at each vertex. It can be constructed as the pyramid product of 2 regular pentagrams with a height chosen so that all edge lengths are equal.

Vertex coordinates
The vertices of a pentagrammic disphenoid of edge length 1 are given by:
 * $$\left(±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}},\,0,\,0,\,\frac{1}{2\sqrt[4]{5}}\right),$$
 * $$\left(±\frac{\sqrt5-1}{4},\,\sqrt{\frac{5+\sqrt5}{40}},\,0,\,0,\,\frac{1}{2\sqrt[4]{5}}\right),$$
 * $$\left(0,\,-\sqrt{\frac{5-\sqrt5}{10}},\,0,\,0,\,\frac{1}{2\sqrt[4]{5}}\right),$$
 * $$\left(0,\,0,\,±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}},\,-\frac{1}{2\sqrt[4]{5}}\right),$$
 * $$\left(0,\,0,\,±\frac{\sqrt5-1}{4},\,\sqrt{\frac{5+\sqrt5}{40}},\,-\frac{1}{2\sqrt[4]{5}}\right),$$
 * $$\left(0,\,0,\,0,\,-\sqrt{\frac{5-\sqrt5}{10}},\,-\frac{1}{2\sqrt[4]{5}}\right).$$