Square-pyritohedral icosahedral duoantiprism

The square-pyritohedral icosahedral duoantiprism is a convex isogonal polyteron that consists of 8 pyritohedral icosahedral antiprisms, 8 triangular-square duoantiprisms, 6 digonal-square duoantiprisms and 96 digonal disphenoidal pyramids obtained through the process of alternating the octagonal-truncated octahedral duoprism. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{24+9\sqrt2}{23}}$$ ≈ 1:1.26367.

Vertex coordinates
The vertices of a square-pyritohedral icosahedral duoantiprism, assuming that the edge length differences are minimized, centered at the origin, are given by: with all even permutations of the first three coordinates, and with all odd permutations of the first three coordinates.
 * (0, ±$\sqrt{6}$/6, ±$\sqrt{6}$/3, 0, ±$\sqrt{2}$/2),
 * (0, ±$\sqrt{6}$/6, ±$\sqrt{6}$/3, ±$\sqrt{2}$/2, 0),
 * (0, ±$\sqrt{6}$/6, ±$\sqrt{6}$/3, ±1/2, ±1/2),
 * (0, ±$\sqrt{6}$/6, ±$\sqrt{6}$/3, ±1/2, ±1/2),