Triangular-great enneagrammic duoprism

The triangular-great enneagrammic duoprism, also known as tagstedip or the 3-9/4 duoprism, is a uniform duoprism that consists of 9 triangular prisms and 3 great enneagrammic prisms, with 2 of each at each vertex.

Vertex coordinates
The coordinates of a triangular-great enneagrammic duoprism, centered at the origin and with edge length 2sin(4π/9), are given by: where j = 2, 4, 8.
 * $$\left(0,\,\frac{2\sqrt3}3\sin\frac{4\pi}9,\,1,\,0\right),$$
 * $$\left(0,\,\frac{2\sqrt3}3\sin\frac{4\pi}9,\,\cos\left(\frac{j\pi}9\right),\,±\sin\left(\frac{j\pi}9\right)\right),$$
 * $$\left(0,\,\frac{2\sqrt3}3\sin\frac{4\pi}9,\,-\frac12,\,±\frac{\sqrt3}2\right),$$
 * $$\left(±\sin\frac{4\pi}9,\,-\frac{\sqrt3}3\sin\frac{4\pi}9,\,1,\,0\right),$$
 * $$\left(±\sin\frac{4\pi}9,\,-\frac{\sqrt3}3\sin\frac{4\pi}9,\,\cos\left(\frac{j\pi}9\right),\,±\sin\left(\frac{j\pi}9\right)\right),$$
 * $$\left(±\sin\frac{4\pi}9,\,-\frac{\sqrt3}3\sin\frac{4\pi}9,\,-\frac12,\,±\frac{\sqrt3}2\right),$$