Small triangular double gyroprismantiprismoid

The triangular double antiprismoid is a convex isogonal polychoron and the second member of the double prismantiprismoids that consists of 12 triangular antiprisms, 12 triangular prisms, 18 cuboids, 72 trapezoidal pyramids, 18 tetragonal disphenoids and 36 digonal disphenoids obtained as the convex hull of two orthogonal triangular-triangular duoantiprisms. However, it cannot be made scaliform.

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:
 * (0, $\sqrt{3}$/3, ±1/2, $\sqrt{51+36√2}$/6)
 * (0, $\sqrt{3}$/3, ±(2+$\sqrt{2}$)/2, -$\sqrt{6}$/6)
 * (0, $\sqrt{3}$/3, ±(1+$\sqrt{2}$)/2, -$\sqrt{33+18√2}$/6)
 * (0, -$\sqrt{3}$/3, ±1/2, -$\sqrt{51+36√2}$/6)
 * (0, -$\sqrt{3}$/3, ±(2+$\sqrt{2}$)/2, $\sqrt{6}$/6)
 * (0, -$\sqrt{3}$/3, ±(1+$\sqrt{2}$)/2, $\sqrt{33+18√2}$/6)
 * (±1/2, -$\sqrt{3}$/6, ±1/2, $\sqrt{51+36√2}$/6)
 * (±1/2, -$\sqrt{3}$/6, ±(2+$\sqrt{2}$)/2, -$\sqrt{6}$/6)
 * (±1/2, -$\sqrt{3}$/6, ±(1+$\sqrt{2}$)/2, -$\sqrt{33+18√2}$/6)
 * (±1/2, $\sqrt{3}$/6, ±1/2, -$\sqrt{51+36√2}$/6)
 * (±1/2, $\sqrt{3}$/6, ±(2+$\sqrt{2}$)/2, $\sqrt{6}$/6)
 * (±1/2, $\sqrt{3}$/6, ±(1+$\sqrt{2}$)/2, $\sqrt{33+18√2}$/6)
 * (±1/2, $\sqrt{51+36√2}$/6, 0, $\sqrt{3}$/3)
 * (±1/2, -$\sqrt{51+36√2}$/6, 0, -$\sqrt{3}$/3)
 * (±1/2, $\sqrt{51+36√2}$/6, ±1/2, -$\sqrt{3}$/6)
 * (±1/2, -$\sqrt{51+36√2}$/6, ±1/2, $\sqrt{3}$/6)
 * (±(1+$\sqrt{2}$)/2, -$\sqrt{33+18√2}$/6, 0, $\sqrt{3}$/3)
 * (±(1+$\sqrt{2}$)/2, $\sqrt{33+18√2}$/6, 0, -$\sqrt{3}$/3)
 * (±(1+$\sqrt{2}$)/2, -$\sqrt{33+18√2}$/6, ±1/2, -$\sqrt{3}$/6)
 * (±(1+$\sqrt{2}$)/2, $\sqrt{33+18√2}$/6, ±1/2, $\sqrt{3}$/6)
 * (±(2+$\sqrt{2}$)/2, -$\sqrt{6}$/6, 0, $\sqrt{3}$/3)
 * (±(2+$\sqrt{2}$)/2, $\sqrt{6}$/6, 0, -$\sqrt{3}$/3)
 * (±(2+$\sqrt{2}$)/2, -$\sqrt{6}$/6, ±1/2, -$\sqrt{3}$/6)
 * (±(2+$\sqrt{2}$)/2, $\sqrt{6}$/6, ±1/2, $\sqrt{3}$/6)