Pyritosnub alterprism

The pyritosnub alterprism, also known as the edge-snub octahedral hosochoron or pysna, is a convex isogonal polychoron that consists of 2 pyritohedral small rhombicuboctahedra, 6 rectangular trapezoprisms, 8 triangular antiprisms and 24 wedges obtained through the process of edge-alternating the great rhombicuboctahedral prism. However, it cannot be made uniform.

Vertex coordinates
The vertices of a pyritosnub alterprism, assuming that the triangular antiprisms are regular of edge length 1 and are a unit distance apart, centered at the origin, are given by the cyclic permutations excluding the last coordinate of:


 * (±1/2, ±(3+$\sqrt{6}$)/6, ±(3+2$\sqrt{6}$)/6, $\sqrt{6}$/6)
 * (±1/2, ±(3+2$\sqrt{6}$)/6, ±(3+$\sqrt{6}$)/6, –$\sqrt{6}$/6)

An alternate set of coordinates, assuming that the edge length differences are minimized, centered at the origin, are given by the cyclic permutations excluding the last coordinate of:


 * (±1/2, ±c1, ±c2, c3)
 * (±1/2, ±c2, ±c1, –c3)

where


 * $$c_1=\text{root}(208x^4-192x^3-24x^2+32x+5,\, 3) ≈ 0.6545479408664677382876785,$$
 * $$c_2=\text{root}(208x^4-256x^3-24x^2+16x+1,\, 4) ≈ 1.2715982466042828483994902,$$
 * $$c_3=\text{root}(10816x^8-4544x^6+352x^4+32x^2-1,\, 6) ≈ 0.4879113310704798497401873.$$