Square-dodecagrammic duoprism

The square-dodecagrammic duoprism, also known as the 4-12/5 duoprism, is a uniform duoprism that consists of 12 cubes and 4 dodecagrammic prisms, with 2 of each at each vertex.

Vertex coordinates
The vertex coordinates of a square-dodecagrammic duoprism, centered at the origin and with unit edge length, are given by:
 * $$\left(±\frac12,\,±\frac12,\,±\frac{\sqrt3-1}2,\,±\frac{\sqrt3-1}2\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{2-\sqrt3}2,\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac12,\,±\frac{2-\sqrt3}2\right).$$

Representations
A square-dodecagrammic duoprism has the following Coxeter diagrams:
 * x4o x12/5o (full symmetry)
 * x x x12/5o (I2(12)×I×I symmetry, dodecagrammic prismatic prism)