Triangular duoantiprismatic antiprism

The triangular duoantiprismatic antiprism is a convex isogonal polyteron that consists of 2 triangular duoantiprisms, 12 digonal-triangular duoantiprisms and 36 tetragonal disphenoidal pyramids obtained through the process of alternating the hexagonal duoprismatic prism. However, it cannot be made uniform.

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