Snub tesseractic antiprism

The snub tesseractic antiprism or snettap is a convex isogonal polyteron that consists of 2 snub tesseracts, 8 snub cubic antiprisms, 16 snub tetrahedral antiprisms, 24 digonal-square duoantiprisms, 32 digoanl-triangular duoantiprisms, and 384 irregular pentachora. 5 pentachora and one of each of the other cell types join at each vertex. It can be obtained through the process of alternating the great disprismatotesseractihexadecachoric prism. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:a ≈ 1:1.25002, where a is the largest real root of 5329x12-23652x10+41382x8-37052x6+18052x4-4560x2+468.

Vertex coordinates
Vertex coordinates for a snub tesseractic antiprism, assuming that the edge length differences are minimized, 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 except the last coordinate of:


 * $$\left(c_1,\,c_2,\,c_3,\,c_4,\,c_5\right),$$
 * $$\left(c_2,\,c_1,\,c_3,\,c_4,\,-c_5\right),$$

where


 * $$c_1≈0.3191085335012948850450705,$$
 * $$c_2≈0.6310069285250780509169974,$$
 * $$c_3≈0.9720792302282349822564494,$$
 * $$c_4≈1.4440010653634313903563943,$$
 * $$c_5≈0.3336991298140972819894887.$$