Snub prismatotriacontaditeron

The snub prismatotriacontaditeron or spitac, also commonly called the omnisnub demipenteract, is a convex isogonal polyteron obtained through the process of alternating the great prismated triacontaditeron. However, it cannot be made uniform.

Unlike the related icosahedron and snub disicositetrachoron, which both possess central inversion symmetry, this polyteron has no such symmetry.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$\sqrt{9+3√2}$/3 ≈ 1:1.21301.

Vertex coordinates
The vertices of a snub prismatotriacontaditeron, assuming that the edge length differences are minimized via the absolute value method, centered at the origin, are given by all even permutations and all sign changes of:


 * (0, 1/2, (3+$\sqrt{6}$)/6, (3+2$\sqrt{6}$)/6, (3+$\sqrt{6}$)/3).

Another set of coordinates for a snub prismatotriacontaditeron, using the ratio method, centered at the origin, are given by all even permutations and all sign changes of:


 * (0, 1/2, (2+$\sqrt{2}$)/4, (1+$\sqrt{2}$)/2, (2+$\sqrt{2}$)/2).