Decagonal-dodecagrammic duoprism

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

Vertex coordinates
The coordinates of a decagonal-dodecagrammic duoprism, centered at the origin and with unit edge length, are given by:
 * $$\left(±\frac12,\,±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac{\sqrt3-1}2,\,±\frac{\sqrt3-1}2\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,±\frac{2-\sqrt3}2\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac{2-\sqrt3}2,\,±\frac12\right),$$
 * $$\left(±\frac{3+\sqrt5}4,\,±\sqrt{\frac{5+\sqrt5}8},\,±\frac{\sqrt3-1}2,\,±\frac{\sqrt3-1}2\right),$$
 * $$\left(±\frac{3+\sqrt5}4,\,±\sqrt{\frac{5+\sqrt5}8},\,±\frac12,\,±\frac{2-\sqrt3}2\right),$$
 * $$\left(±\frac{3+\sqrt5}4,\,±\sqrt{\frac{5+\sqrt5}8},\,±\frac{2-\sqrt3}2,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt5}2,\,0,\,±\frac{\sqrt3-1}2,\,±\frac{\sqrt3-1}2\right),$$
 * $$\left(±\frac{1+\sqrt5}2,\,0,\,±\frac12,\,±\frac{2-\sqrt3}2\right),$$
 * $$\left(±\frac{1+\sqrt5}2,\,0,\,±\frac{2-\sqrt3}2,\,±\frac12\right).$$

Representations
A decagonal-dodecagrammic duoprism has the following Coxeter diagrams:
 * x10o x12/5o (full symmetry)
 * x5x x12/5o (H2×I2(12) symmetry, decagons as dipentagons)