Snub disicositetrachoric antiprism

The snub disicositetrachoric antiprism or sadiap, also called the snub rhombatohexadecachoric antiprism or omnisnub demitesseractic antiprism, is a convex isogonal polyteron obtained through the process of alternating the truncated icositetrachoric prism. It cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt{15+\sqrt{17}}}{4}$$ ≈ 1:1.09325.

Vertex coordinates
The vertices of a snub disicositetrachoric antiprism, assuming that the edge length differences are minimized, centered at the origin, are given by the cyclic permutations excluding the last coordinate of:


 * (0, ±1/2, ±(3+$\sqrt{17}$)/8, ±(7+$\sqrt{17}$)/8, $\sqrt{7+√17}$/8).
 * (0, ±(3+$\sqrt{17}$)/8, ±1/2, ±(7+$\sqrt{17}$)/8, -$\sqrt{7+√17}$/8).