Great enneagrammic-decagonal duoprism

The great enneagrammic-decagonal duoprism, also known as gistdedip or the 9/4-10 duoprism, is a uniform duoprism that consists of 10 great enneagrammic prisms and 9 decagonal prisms, with 2 of each at each vertex.

Vertex coordinates
The coordinates of a great enneagrammic-decagonal duoprism, centered at the origin and with edge length 2sin(4π/9), are given by: where j = 2, 4, 8.
 * $$\left(1,\,0,\,±\sin\frac{4\pi}9,\,±\sqrt{5+2\sqrt5}\sin\frac{4\pi}9\right),$$
 * $$\left(1,\,0,\,±\frac{3+\sqrt5}2\sin\frac{4\pi}9,\,±\sqrt{\frac{5+\sqrt5}2}\sin\frac{4\pi}9\right),$$
 * $$\left(1,\,0,\,±\left(1+\sqrt5\right)\sin\frac{4\pi}9,\,0\right),$$
 * $$\left(\cos\left(\frac{j\pi}9\right),\,±\sin\left(\frac{j\pi}9\right),\,±\sin\frac{4\pi}9,\,±\sqrt{5+2\sqrt5}\sin\frac{4\pi}9\right),$$
 * $$\left(\cos\left(\frac{j\pi}9\right),\,±\sin\left(\frac{j\pi}9\right),\,±\frac{3+\sqrt5}2\sin\frac{4\pi}9,\,±\sqrt{\frac{5+\sqrt5}2}\sin\frac{4\pi}9\right),$$
 * $$\left(\cos\left(\frac{j\pi}9\right),\,±\sin\left(\frac{j\pi}9\right),\,±\left(1+\sqrt5\right)\sin\frac{4\pi}9,\,0\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,±\sin\frac{4\pi}9,\,±\sqrt{5+2\sqrt5}\sin\frac{4\pi}9\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,±\frac{3+\sqrt5}2\sin\frac{4\pi}9,\,±\sqrt{\frac{5+\sqrt5}2}\sin\frac{4\pi}9\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,±\left(1+\sqrt5\right)\sin\frac{4\pi}9,\,0\right),$$

Representations
A great enneagrammic-decagonal duoprism has the following Coxeter diagrams:
 * x9/4o x10o (full symmetry)
 * x5x x9/4o (H2×I2(9) symmetry, decagons as dipentagons)