Pentagonal-octagrammic duoprism

The pentagonal-octagrammic duoprism, also known as pistodip or the 5-8/3 duoprism, is a uniform duoprism that consists of 8 pentagonal prisms and 5 octagrammic prisms, with 2 of each at each vertex.

Vertex coordinates
The coordinates of a pentagonal-octagrammic duoprism, centered at the origin and with edge length 1, are given by:
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac12,\,±\frac{\sqrt2-1}2\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac{\sqrt2-1}2,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac12,\,±\frac{\sqrt2-1}2\right),$$
 * $$\left(±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac{\sqrt2-1}2,\,±\frac12\right),$$
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac12,\,±\frac{\sqrt2-1}2\right),$$
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac{\sqrt2-1}2,\,±\frac12\right).$$