Triangular-square duoantiprismatic antiprism

The triangular-square duoantiprismatic antiprism is a convex isogonal polyteron that consists of 2 triangular-square duoantiprisms, 6 digonal-square duoantiprisms, 8 digonal-triangular duoantiprisms and 48 digonal disphenoidal pyramids obtained through the process of alternating the hexagonal-octagonal duoprismatic prism. However, it cannot be made uniform.

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