Snub tetrahedral alterprism

The snub tetrahedral alterprism or snita is a convex isogonal polychoron that consists of 2 snub tetrahedra, 8 chiral triangular antipodiums, 6 rhombic disphenoids, 12 phyllic disphenoids, and 24 irregular tetrahedra. 1 snub tetrahedron, 2 triangular antipodiums, 1 rhombic disphenoid, 2 phyllic disphenoids, and 4 irregular tetrahedra join at each vertex. 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, using the absolute value method, centered at the origin, are given by the cyclic permutations and even sign changes excluding the last coordinate of:
 * $$±\left(\frac{\sqrt5}{10},\,\frac{\sqrt5}{5},\,\sqrt{\frac{11+3\sqrt{13}}{40}},\,\frac{\sqrt5}{10}\right).$$

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, c2),

where


 * $$c_1=\text{root}(128x^6-112x^4+28x^2-1, 2) ≈ 0.2064681930961176888694291,$$
 * $$c_2=\text{root}(128x^6+16x^4-4x^2-1, 2) ≈ 0.4553799350428433840815926,$$
 * $$c_3=\text{root}(128x^6-144x^4+16x^2-1, 2) ≈ 1.0043720639483018983297714.$$