Small triangular double gyroprismantiprismoid

The triangular double prismantiprismoid is a convex isogonal polychoron and the second member of the double prismantiprismoid family. It consists of 12 triangular antiprisms, 12 triangular prisms, 18 rectangular trapezoprisms, 72 isosceles trapezoidal pyramids, 18 tetragonal disphenoids, and 36 digonal disphenoids. 1 triangular antiprism, 1 triangular prism, 2 rectangular trapezoprisms, 5 isosceles trapezoidal pyramids, 1 tetragonal disphenoid, and 2 digonal disphenoids join at each vertex. It can be obtained as the convex hull of two orthogonal triangular-hexagonal prismantiprismoids. However, it cannot be made scaliform.

A variant with regular octahedra and uniform triangular prisms can be vertex-inscribed into a small prismatotetracontoctachoron.

Vertex coordinates
The vertices of a triangular double prismantiprismoid, assuming that the triangular antiprisms and triangular prisms are uniform of edge length 1, centered at the origin, are given by:
 * $$\left(0,\,\frac{\sqrt3}{3},\,±\frac12,\,\frac{3\sqrt3+2\sqrt6}{6}\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,±\frac{2+\sqrt2}{2},\,-\frac{\sqrt6}{6}\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,±\frac{1+\sqrt2}{2},\,-\frac{3\sqrt3+\sqrt6}{6}\right),$$
 * $$\left(0,\,-\frac{\sqrt3}{3},\,±\frac12,\,-\frac{3\sqrt3+2\sqrt6}{6}\right),$$
 * $$\left(0,\,-\frac{\sqrt3}{3},\,±\frac{2+\sqrt2}{2},\,\frac{\sqrt6}{6}\right),$$
 * $$\left(0,\,-\frac{\sqrt3}{3},\,±\frac{1+\sqrt2}{2},\,\frac{3\sqrt3+\sqrt6}{6}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12,\,\frac{3\sqrt3+2\sqrt6}{6}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac{2+\sqrt2}{2},\,-\frac{\sqrt6}{6}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac{1+\sqrt2}{2},\,-\frac{3\sqrt3+\sqrt6}{6}\right),$$
 * $$\left(±\frac12,\,\frac{\sqrt3}{6},\,±\frac12,\,-\frac{3\sqrt3+2\sqrt6}{6}\right),$$
 * $$\left(±\frac12,\,\frac{\sqrt3}{6},\,±\frac{2+\sqrt2}{2},\,\frac{\sqrt6}{6}\right),$$
 * $$\left(±\frac12,\,\frac{\sqrt3}{6},\,±\frac{1+\sqrt2}{2},\,\frac{3\sqrt3+\sqrt6}{6}\right),$$
 * $$\left(±\frac12,\,\frac{3\sqrt3+2\sqrt6}{6},\,0,\,\frac{\sqrt3}{3}\right),$$
 * $$\left(±\frac12,\,-\frac{3\sqrt3+2\sqrt6}{6},\,0,\,-\frac{\sqrt3}{3}\right),$$
 * $$\left(±\frac12,\,\frac{3\sqrt3+2\sqrt6}{6},\,±\frac12,,\,-\frac{\sqrt3}{6}\right),$$
 * $$\left(±\frac12,\,-\frac{3\sqrt3+2\sqrt6}{6},\,±\frac12,\,\frac{\sqrt3}{6}\right),$$
 * $$\left(±\frac{1+\sqrt2}{2},\,-\frac{3\sqrt3+\sqrt6}{6},\,0,\,\frac{\sqrt3}{3}\right),$$
 * $$\left(±\frac{1+\sqrt2}{2},\,\frac{3\sqrt3+\sqrt6}{6},\,0,\,-\frac{\sqrt3}{3}\right),$$
 * $$\left(±\frac{1+\sqrt2}{2},\,-\frac{3\sqrt3+\sqrt6}{6},\,±\frac12,\,-\frac{\sqrt3}{6}\right),$$
 * $$\left(±\frac{1+\sqrt2}{2},\,\frac{3\sqrt3+\sqrt6}{6},\,±\frac12,\,\frac{\sqrt3}{6}\right),$$
 * $$\left(±\frac{2+\sqrt2}{2},\,-\frac{\sqrt6}{6},\,0,\,\frac{\sqrt3}{3}\right),$$
 * $$\left(±\frac{2+\sqrt2}{2},\,\frac{\sqrt6}{6},\,0,\,-\frac{\sqrt3}{3}\right),$$
 * $$\left(±\frac{2+\sqrt2}{2},\,-\frac{\sqrt6}{6},\,±\frac12,,\,-\frac{\sqrt3}{6}\right),$$
 * $$\left(±\frac{2+\sqrt2}{2},\,\frac{\sqrt6}{6},\,±\frac12,\,\frac{\sqrt3}{6}\right).$$