Triangular trioantiprism

The triangular trioantiprism is a convex isogonal polypeton that consists of 18 triangular duoantiprismatic antiprisms and 108 digonal trisphenoids obtained through the process of alternating the hexagonal trioprism. However, it cannot be made uniform.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt6}{2}$$ ≈ 1:1.22474.

Vertex coordinates
The vertices of a triangular trioantiprism, created from the vertices of a hexagonal trioprism of edge length $\sqrt{3}$/3, centered at the origin, are given by:
 * (0, $\sqrt{3}$/3, 0, $\sqrt{3}$/3, 0, $\sqrt{3}$/3),
 * (0, $\sqrt{3}$/3, 0, $\sqrt{3}$/3, ±1/2, -$\sqrt{3}$/6),
 * (0, -$\sqrt{3}$/3, 0, -$\sqrt{3}$/3, 0, $\sqrt{3}$/3),
 * (0, -$\sqrt{3}$/3, 0, -$\sqrt{3}$/3, ±1/2, -$\sqrt{3}$/6),
 * (0, $\sqrt{3}$/3, ±1/2, -$\sqrt{3}$/6, 0, $\sqrt{3}$/3),
 * (0, $\sqrt{3}$/3, ±1/2, -$\sqrt{3}$/6, ±1/2, -$\sqrt{3}$/6),
 * (0, -$\sqrt{3}$/3, ±1/2, $\sqrt{3}$/6, 0, $\sqrt{3}$/3),
 * (0, -$\sqrt{3}$/3, ±1/2, $\sqrt{3}$/6, ±1/2, -$\sqrt{3}$/6),
 * (±1/2, -$\sqrt{3}$/6, 0, $\sqrt{3}$/3, 0, $\sqrt{3}$/3),
 * (±1/2, -$\sqrt{3}$/6, 0, $\sqrt{3}$/3, ±1/2, -$\sqrt{3}$/6),
 * (±1/2, $\sqrt{3}$/6, 0, -$\sqrt{3}$/3, 0, $\sqrt{3}$/3),
 * (±1/2, $\sqrt{3}$/6, 0, -$\sqrt{3}$/3, ±1/2, -$\sqrt{3}$/6),
 * (±1/2, $\sqrt{3}$/6, ±1/2, $\sqrt{3}$/6, 0, $\sqrt{3}$/3),
 * (±1/2, $\sqrt{3}$/6, ±1/2, $\sqrt{3}$/6, ±1/2, -$\sqrt{3}$/6),
 * (±1/2, -$\sqrt{3}$/6, ±1/2, -$\sqrt{3}$/6, 0, $\sqrt{3}$/3),
 * (±1/2, -$\sqrt{3}$/6, ±1/2, -$\sqrt{3}$/6, ±1/2, -$\sqrt{3}$/6),
 * (0, $\sqrt{3}$/3, 0, -$\sqrt{3}$/3, 0, -$\sqrt{3}$/3),
 * (0, $\sqrt{3}$/3, 0, -$\sqrt{3}$/3, ±1/2, $\sqrt{3}$/6),
 * (0, -$\sqrt{3}$/3, 0, $\sqrt{3}$/3, 0, -$\sqrt{3}$/3),
 * (0, -$\sqrt{3}$/3, 0, $\sqrt{3}$/3, ±1/2, $\sqrt{3}$/6),
 * (0, $\sqrt{3}$/3, ±1/2, $\sqrt{3}$/6, 0, -$\sqrt{3}$/3),
 * (0, $\sqrt{3}$/3, ±1/2, $\sqrt{3}$/6, ±1/2, $\sqrt{3}$/6),
 * (0, -$\sqrt{3}$/3, ±1/2, -$\sqrt{3}$/6, 0, -$\sqrt{3}$/3),
 * (0, -$\sqrt{3}$/3, ±1/2, -$\sqrt{3}$/6, ±1/2, $\sqrt{3}$/6),
 * (±1/2, $\sqrt{3}$/6, 0, $\sqrt{3}$/3, 0, -$\sqrt{3}$/3),
 * (±1/2, $\sqrt{3}$/6, 0, $\sqrt{3}$/3, ±1/2, $\sqrt{3}$/6),
 * (±1/2, -$\sqrt{3}$/6, 0, -$\sqrt{3}$/3, 0, -$\sqrt{3}$/3),
 * (±1/2, -$\sqrt{3}$/6, 0, -$\sqrt{3}$/3, ±1/2, $\sqrt{3}$/6),
 * (±1/2, $\sqrt{3}$/6, ±1/2, -$\sqrt{3}$/6, 0, -$\sqrt{3}$/3),
 * (±1/2, $\sqrt{3}$/6, ±1/2, -$\sqrt{3}$/6, ±1/2, $\sqrt{3}$/6),
 * (±1/2, -$\sqrt{3}$/6, ±1/2, $\sqrt{3}$/6, 0, -$\sqrt{3}$/3),
 * (±1/2, -$\sqrt{3}$/6, ±1/2, $\sqrt{3}$/6, ±1/2, $\sqrt{3}$/6).