Snub tetrahedral alterprism

The snub tetrahedral alterprism or snita is a convex isogonal polychoron that consists of 2 snub tetrahedra, 8 triangular antipodiums, 6 rhombic disphenoids, 12 phyllic disphenoids and 24 irregular tetrahedra. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:a ≈ 1:1.48512, where a is the positive real root of x6-2x4-1.

Vertex coordinates
Coordinates for the vertices of a snub tetrahedral alterprism, assuming that the edge length differences are minimized, centered at the origin, are given by the cyclic permutations and even sign changes excluding the last coordinate of:
 * ±($\sqrt{5}$/10, $\sqrt{5}$/5, $\sqrt{110+30√13}$/20, $\sqrt{5}$/10).

Another set of coordinates for the vertices of a snub tetrahedral alterprism, assuming that the ratio method is used, centered at the origin, are given by the cyclic permutations and even sign changes excluding the last coordinate of:
 * (c1, c2, c3, c1),

where


 * $$c_1=\text{root}(128x^6-112x^4+28x^2-1, 2) ≈ 0.2064681930961176888694291,$$
 * $$c_2=\text{root}(128x^6+16x^4-4x^2-1, 2) ≈ 0.6542869462841313854118897,$$
 * $$c_3=\text{root}(128x^6-144x^4+16x^2-1, 2) ≈ 1.0043720639483018983297714.$$