Triangular double antiprismoid

The triangular double antiprismoid is a convex isogonal polychoron and the second member of the double antiprismoids that consists of 12 triangular antiprisms, 36 tetragonal disphenoids and 72 sphenoids obtained as the convex hull of two orthogonal triangular-triangular duoantiprisms. However, it cannot be made uniform. Together with its dual, it is the first in an infinite family of triangular antiprismatic swirlchora.

The triangular double antiprismoid can be vertex-inscribed into a tetradisphenoidal diacosioctacontoctachoron.

Vertex coordinates
The vertices of a triangular double antiprismoid, assuming that the octahedra are regular of edge length 1, centered at the origin, are given by:
 * (0, $\sqrt{3}$/3, 0, $\sqrt{6}$/3),
 * (0, -$\sqrt{3}$/3, 0, -$\sqrt{6}$/3),
 * (0, $\sqrt{3}$/3, ±$\sqrt{2}$/2, -$\sqrt{6}$/6),
 * (0, -$\sqrt{3}$/3, ±$\sqrt{2}$/2, $\sqrt{6}$/6),
 * (±1/2, -$\sqrt{3}$/6, 0, $\sqrt{6}$/3),
 * (±1/2, $\sqrt{3}$/6, 0, -$\sqrt{6}$/3),
 * (±1/2, $\sqrt{3}$/6, ±$\sqrt{2}$/2, $\sqrt{6}$/6),
 * (±1/2, -$\sqrt{3}$/6, ±$\sqrt{2}$/2, -$\sqrt{6}$/6),
 * (0, $\sqrt{6}$/3, 0, $\sqrt{3}$/3),
 * (0, -$\sqrt{6}$/3, 0, -$\sqrt{3}$/3),
 * (0, $\sqrt{6}$/3, ±1/2, -$\sqrt{3}$/6),
 * (0, -$\sqrt{6}$/3, ±1/2, $\sqrt{3}$/6),
 * (±$\sqrt{2}$/2, -$\sqrt{6}$/6, 0, $\sqrt{3}$/3),
 * (±$\sqrt{2}$/2, $\sqrt{6}$/6, 0, -$\sqrt{3}$/3),
 * (±$\sqrt{2}$/2, $\sqrt{6}$/6, ±1/2, $\sqrt{3}$/6),
 * (±$\sqrt{2}$/2, -$\sqrt{6}$/6, ±1/2, -$\sqrt{3}$/6).