Square-great enneagrammic duoprism

The square-great enneagrammic duoprism, also known as sagstedip or the 4-9/4 duoprism, is a uniform duoprism that consists of 9 cubes and 4 great enneagrammic prisms, with 2 of each at each vertex.

Vertex coordinates
The coordinates of a square-great enneagrammic duoprism, centered at the origin and with edge length 2sin(4π/9), are given by: where j = 2, 4, 8.
 * $$\left(±\sin\frac{4\pi}9,\,±\sin\frac{4\pi}9,\,1,\,0\right),$$
 * $$\left(±\sin\frac{4\pi}9,\,±\sin\frac{4\pi}9,\,\cos\left(\frac{j\pi}9\right),\,±\sin\left(\frac{j\pi}9\right)\right),$$
 * $$\left(±\sin\frac{4\pi}9,\,±\sin\frac{4\pi}9,\,-\frac12,\,±\frac{\sqrt3}2\right),$$

Representations
A square-great enneagrammic duoprism has the following Coxeter diagrams:
 * x4o x9/4o (full symmetry)
 * x x x9/4o (I2(9)×I×I symmetry, great enneagrammic prismatic prism)