Pyritosnub tesseractic alterprism

The pyritosnub tesseractic alterprism or pysneta, also known as the edge-snub hexadecachoric hosoteron, is a convex isogonal polyteron that consists of 2 pyritosnub tesseracts, 8 pyritosnub alterprisms, 16 snub tetrahedral antiprisms, 32 triangular gyroprismatic prisms, 24 digonal-rectangular prismantiprismoids, and 192 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 disprismatotesseractihexadecachoric prism 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:a ≈ 1:1.49032, where a is the second largest real root of 37x6-50x5-81x4+40x3+80x2+32x+4.

Vertex coordinates
Vertex coordinates for a pyritosnub tesseractic alterprism, assuming that the edge length differences are minimized, using the ratio method, by all even permutations of the first four coordinates of:


 * $$\left(±\frac12,\,±c_1,\,±c_2,\,±c_3,\,\frac12\right),$$
 * $$\left(±\frac12,\,±c_1,\,±c_3,\,±c_2,\,-\frac12\right),$$

where


 * $$c_1=\text{root}(592x^6-400x^5-324x^4+80x^3+80x^2+16x+1,\ 3) ≈ 0.7451616366591140373440626,$$
 * $$c_2=\text{root}(2368x^6-3392x^5+160x^4+384x^3-56x^2-16x+1,\ 4) ≈ 1.2970597497521540982365781,$$
 * $$c_3=\text{root}(2368x^6-3264x^5-2848x^4+288x^3+56x^2-112x+1,\ 4) ≈ 1.9603061382916052138473956.$$