Triangular-square duoantiprism

The triangular-square duoantiprism, also known as the 3-4 duoantiprism, is a convex isogonal polychoron that consists of 6 square antiprisms, 8 triangular antiprisms and 24 digonal disphenoids obtained through the process of alternating the hexagonal-octagonal duoprism. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$\sqrt{552+207√2}$/23 ≈ 1:1.26367.

Vertex coordinates
The vertices of a triangular-square duoantiprism, assuming that the square antiprisms are regular of edge length 1, centered at the origin, are given by:
 * (±1/2, ±1/2, 0, $\sqrt$/2),
 * (±1/2, ±1/2, ±$\sqrt$/4, -$\sqrt$/4),
 * (0, ±$\sqrt{2}$/2, 0, -$\sqrt$/2),
 * (0, ±$\sqrt{2}$/2, ±$\sqrt$/4, $\sqrt$/4),
 * (±$\sqrt{2}$/2, 0, 0, -$\sqrt$/2),
 * (±$\sqrt{2}$/2, 0, ±$\sqrt$/4, $\sqrt$/4).

An alternate set of coordinates, assuming that the edge length differences are minimized, centered at the origin, are given by:
 * (±1/2, ±1/2, 0, $\sqrt{3}$/3),
 * (±1/2, ±1/2, ±1/2, -$\sqrt{3}$/6),
 * (0, ±$\sqrt{2}$/2, 0, -$\sqrt{3}$/3),
 * (0, ±$\sqrt{2}$/2, ±1/2, $\sqrt{3}$/6),
 * (±$\sqrt{2}$/2, 0, 0, -$\sqrt{3}$/3),
 * (±$\sqrt{2}$/2, 0, ±1/2, $\sqrt{3}$/6).