Snub penteract

The snub penteract or snan is a convex isogonal polyteron that consists of 10 snub tesseract, 32 snub pentachora, 40 snub cubic antiprisms, 80 snub tetrahedral antiprisms, 80 triangular-square duoantiprisms, and 1920 iregular pentachora. 5 pentachora and 1 of each of the other facet types join at each vertex. It can be obtained through the process of alternating the great cellipenteractitriacontaditeron. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\sqrt{\frac{24+9\sqrt2}{23}}$$ ≈ 1:1.26367.

Vertex coordinates
Coordinates for the vertices of an optimized snub penteract. using the ratio method, are given by all even permutations with an even number of sign changes, plus all odd permutations with an odd amount of sign changes, of:
 * $$\left(\sqrt{\frac{2-\sqrt2}{8}},\,\sqrt{\frac{2+\sqrt2}{8}},\,\sqrt{\frac{10+3\sqrt2+4\sqrt{6+3\sqrt2}}{24}},\,\sqrt{\frac{22+3\sqrt2+8\sqrt{6+3\sqrt2}}{24}},\,\frac{\sqrt{14+\sqrt2+4\sqrt{6+3\sqrt2}}{8}}\right).$$