Decagrammic-dodecagrammic duoprism

The decagrammic-dodecagrammic duoprism, also known as the 10/3-12/5 duoprism, is a uniform duoprism that consists of 12 decagrammic prisms and 10 dodecagrammic prisms, with 2 of each at each vertex.

Coordinates
The vertex coordinates of a decagrammic-dodecagrammic duoprism, centered at the origin and with unit edge length, are given by:


 * $$\left(±\frac12,\,±\frac{\sqrt{5-2\sqrt5}}{2},\,±\frac{\sqrt3-1}{2},\,±\frac{\sqrt3-1}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt{5-2\sqrt5}}{2},\,±\frac12,\,±\frac{2-\sqrt3}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt{5-2\sqrt5}}{2},\,±\frac{2-\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\sqrt{\frac{5-\sqrt5}{8}},\,±\frac{\sqrt3-1}{2},\,±\frac{\sqrt3-1}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\sqrt{\frac{5-\sqrt5}{8}},\,±\frac12,\,±\frac{2-\sqrt3}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\sqrt{\frac{5-\sqrt5}{8}},\,±\frac{2-\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,0,\,±\frac{\sqrt3-1}{2},\,±\frac{\sqrt3-1}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,0,\,±\frac12,\,±\frac{2-\sqrt3}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,0,\,±\frac{2-\sqrt3}{2},\,±\frac12\right).$$