Pentagonal-pentagrammic duoprism

The pentagonal-pentagrammic duoprism, also known as starpedip or the 5-5/2 duoprism, is a uniform duoprism that consists of 5 pentagonal prisms and 5 pentagrammic prisms, with 2 of each at each vertex.

This is the only duoprism aside from the tesseract to have a circumradius equal to its edge length.

The pentagonal-pentagrammic duoprism can be edge-inscribed into the small stellated hecatonicosachoron. The small stellated hecatonicosachoron's regiment contains a uniform compound of 24 pentagonal-pentagrammic duoprisms.

Vertex coordinates
The coordinates of a pentagonal-pentagrammic duoprism, centered at the origin and with unit edge length, are given by:
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,0,\,\sqrt{\frac{5-\sqrt5}{10}}\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac{\sqrt5-1}{4},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}}\right),$$
 * $$\left(±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,0,\,\sqrt{\frac{5-\sqrt5}{10}}\right),$$
 * $$\left(±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac{\sqrt5-1}{4},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}}\right),$$
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,0,\,\sqrt{\frac{5-\sqrt5}{10}}\right),$$
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac{\sqrt5-1}{4},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$$
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}}\right),$$