Snub dodecateron

The snub dodecateron or snod, also commonly called the omninsub hexateron or omnisnub 5-simplex, is a convex isogonal polyteron that consists of 12 snub pentachora, 30 snub tetrahedral antiprisms, 20 triangular duoantiprisms, and 360 phyllic disphenoidal pyramids. 2 snub pentachora, 2 snub tetrahedral antiprisms, 1 triangular duoantiprism, and 5 phyllic disphenoidal pyramids join at each vertex. It can be obtained through the process of alternating the great cellidodecateron. However, it cannot be made uniform.

Unlike the related icosahedron and snub decachoron, which both possess central inversion symmetry, this polyteron has no such symmetry.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt6}{2}$$ ≈ 1:1.22474.

Vertex coordinates
The vertices of a snub dodecateron can be given in six dimensions for an optimized snub dodecateron, as all even permutations of:

using the absolute value method, or: using the ratio method (corresponding to the alternation of the uniform great cellidodecateron).
 * $$\left(0,\,\frac12,\,\frac{14+\sqrt{238-34\sqrt{17}}}{28},\,\frac{14+\sqrt{266+42\sqrt{37}}}{28},\,\frac{7+\sqrt{182+21\sqrt{37}}}{14},\,\frac{14+\sqrt{182+21\sqrt{37}}}{14}\right),$$
 * $$\left(0,\,\frac12,\,1,\,\frac32,\,2,\,\frac52\right),$$