Pentagonal-dodecagrammic duoprism

The pentagonal-dodecagrammic duoprism, also known the 5-12/5 duoprism, is a uniform duoprism that consists of 12 pentagonal prisms and 5 dodecagrammic prisms, with two of each at each vertex.

Vertex coordinates
The coordinates of a pentagonal-dodecagrammic duoprism, centered at the origin and with unit edge length, are given by:
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac{\sqrt3-1}2,\,±\frac{\sqrt3-1}2\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac12,\,±\frac{2-\sqrt3}2\right),$$
 * $$\left(±\frac12,\,-\sqrt{\frac{5+2\sqrt5}{20}},\,±\frac{2-\sqrt3}2,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac{\sqrt3-1}2,\,±\frac{\sqrt3-1}2\right),$$
 * $$\left(±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac12,\,±\frac{2-\sqrt3}2\right),$$
 * $$\left(±\frac{1+\sqrt5}4,\,\sqrt{\frac{5-\sqrt5}{40}},\,±\frac{2-\sqrt3}2,\,±\frac12\right),$$
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac{\sqrt3-1}2,\,±\frac{\sqrt3-1}2\right),$$
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac12,\,±\frac{2-\sqrt3}2\right),$$
 * $$\left(0,\,\sqrt{\frac{5+\sqrt5}{10}},\,±\frac{2-\sqrt3}2,\,±\frac12\right).$$