Triangular duoantiprism

The triangular duoantiprism, also known as the triangular-triangular duoantiprism, the 3 duoantiprism or the 3-3 duoantiprism, is a convex isogonal polychoron that consists of 12 triangular antiprisms and 18 tetragonal disphenoids obtained through the process of alternating the hexagonal duoprism. However, it cannot be made uniform. Together with its dual, it is the first in an infinite family of triangular antiprismatic swirlchora.

The ratio between the longest and shortest edges is 1:$\sqrt{6}$/2 ≈ 1:1.22474.

Vertex coordinates
The vertices of a triangular duoantiprism, created from the vertices of a hexagonal duoprism 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, ±1/2, $\sqrt{3}$/6),
 * (±1/2, -$\sqrt{3}$/6, 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, ±1/2, -$\sqrt{3}$/6).

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Triangular antiprism (12): Hexagonal duotegum
 * Tetragonal disphenoid (18): Triangular duoantiprism
 * Triangle (12): Hexagonal duotegum
 * Isosceles triangle (72): Hexagonal ditetragoltriate
 * Edge (36): Hexagonal duoprism
 * Edge (36): Triangular double gyroantiprismoid