Square duotegmatic alterprism

The square duotegmatic alterprism is a convex isogonal polyteron that consists of 2 square duotegums and 32 isosceles triangular-triangular duotegums formed as an alterprism of a square duotegum.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{2+\sqrt2}{2}}$$ ≈ 1:1.30656.

Vertex coordinates
Vertex coordinates for a square duotegmatic alterprism, assuming that the edge length differences are minimized, centered at the origin, are given by:
 * (0, 0, 0, ±$\sqrt{2}$/2, $\sqrt{8|4}$/4),
 * (0, 0, ±$\sqrt{2}$/2, 0, $\sqrt{8|4}$/4),
 * (0, ±$\sqrt{2}$/2, 0, 0, $\sqrt{8|4}$/4),
 * (±$\sqrt{2}$/2, 0, 0, 0, $\sqrt{8|4}$/4),
 * (±1/2, ±1/2, ±1/2, ±1/2, -$\sqrt{8|4}$/4).