Square duoantiprism

The square duoantiprism, also known as the square-square duoantiprism, the 4 duoantiprism or the 4-4 duoantiprism, is a convex isogonal polychoron that consists of 16 square antiprisms and 32 tetragonal disphenoids obtained through the process of alternating the octagonal duoprism. However, it cannot be made uniform. Together with its dual, it is the first in an infinite family of square antiprismatic swirlchora.

The square duoantiprism can be vertex-inscribed into a bitetracontoctachoron.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$\sqrt{4+2√2}$/2 ≈ 1:1.30656.

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