Square trioantiprism

The square trioantiprism is a convex isogonal polypeton that consists of 24 square duoantiprismatic antiprisms and 256 digonal trisphenoids obtained through the process of alternating the octagonal trioprism. However, it cannot be made uniform.

The ratio between the longest and shortest edges is 1:$$\sqrt{\frac{2+\sqrt2}{2}}$$ ≈ 1:1.30656.

Vertex coordinates
The vertices of a square trioantiprism, created from the vertices of an octagonal trioprism of edge length $\sqrt{4-2√2}$/2, centered at the origin, are given by:
 * (±1/2, ±1/2, ±1/2, ±1/2, ±1/2, ±1/2),
 * (0, ±$\sqrt{2}$/2, 0, ±$\sqrt{2}$/2, ±1/2, ±1/2),
 * (0, ±$\sqrt{2}$/2, ±$\sqrt{2}$/2, 0, ±1/2, ±1/2),
 * (±$\sqrt{2}$/2, 0, 0, ±$\sqrt{2}$/2, ±1/2, ±1/2),
 * (±$\sqrt{2}$/2, 0, ±$\sqrt{2}$/2, 0, ±1/2, ±1/2),
 * (±1/2, ±1/2, 0, ±$\sqrt{2}$/2, 0, ±$\sqrt{2}$/2),
 * (±1/2, ±1/2, 0, ±$\sqrt{2}$/2, ±$\sqrt{2}$/2, 0),
 * (±1/2, ±1/2, ±$\sqrt{2}$/2, 0, 0, ±$\sqrt{2}$/2),
 * (±1/2, ±1/2, ±$\sqrt{2}$/2, 0, ±$\sqrt{2}$/2, 0),
 * (0, ±$\sqrt{2}$/2, ±1/2, ±1/2, 0, ±$\sqrt{2}$/2),
 * (0, ±$\sqrt{2}$/2, ±1/2, ±1/2, ±$\sqrt{2}$/2, 0),
 * (±$\sqrt{2}$/2, 0, ±1/2, ±1/2, 0, ±$\sqrt{2}$/2),
 * (±$\sqrt{2}$/2, 0, ±1/2, ±1/2, ±$\sqrt{2}$/2, 0).