Snub disicositetrachoric antiprism

The snub disicositetrachoric antiprism or sadiap, also called the snub rhombatohexadecachoric antiprism or omnisnub demitesseractic antiprism, is a convex isogonal polyteron that consists of 2 snub disicositetrachora, 24 pyritohedral icosahedral antiprisms, 24 tetrahedral antiprisms, and 96 triangular pyramidal pyramids. 1 snub disicositetrachoron, 1 tetrahedral antiprism, 3 pyritohedral icosahedal antiprisms, and 5 triangular pyramidal pyramids join at each vertex. It can be 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:


 * $$\left(0,\,±\frac12,\,±\frac{3+\sqrt{17}}{8},\,±\frac{7+\sqrt{17}}{8},\,\frac{\sqrt{7+\sqrt{17}}}{8}\right),$$
 * $$\left(0,\,±\frac{3+\sqrt{17}}{8},\,±\frac12,\,±\frac{7+\sqrt{17}}{8},\,-\frac{\sqrt{7+\sqrt{17}}}{8}\right).$$