Pyritosnub penteract

The pyritosnub penteract or pysnan, also known as the edge-snub triacontaditeron, is a convex isogonal polyteron that consists of 10 pyritosnub tesseracts, 32 snub pentachora, 40 pyritosnub alterprisms, 80 snub tetrahedral prisms, 80 triangular-square prismantiprismoids, and 960 tetrahedral wedges. 4 tetrahedral wedges and 1 of each of the other facet types join at each vertex. It can be obtained through the process of obtained through the process of edge-alternating the great cellipenteractitriacontaditeron so that the octagons become long rectangles. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{3+2\sqrt6}{5}$$ ≈ 1:1.57980.

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


 * $$\left(\frac{2\sqrt6-3}{6},\,\frac12,\,\frac{3+\sqrt6}{6},\,\frac{3+2\sqrt6}{6},\,\frac{1+\sqrt6}{2}\right).$$