Pyritosnub tesseract

The pyritosnub tesseract or pysnet, also known as the edge-snub hexadecachoron, is a convex isogonal polychoron that consists of 8 pyritohedral small rhombicuboctahedra, 16 snub tetrahedra, 24 rectangular trapezoprisms, 32 triangular prisms and 96 wedges obtained through the process of edge-alternating the great disprismatotesseractihexadecachoron. However, it cannot be made uniform.

A variant with 8 regular icosahedra and 32 uniform triangular prisms can be vertex-inscribed into a prismatorhombisnub icositetrachoron.

Vertex coordinates
The vertices of a pyritosnub tesseract, assuming regular icosahedra and uniform triangular prisms of edge length 1, centered at the origin, are given by all even permutations of:
 * (±1/2, ±1, ±(3+$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4).

An alternate set of coordinates, assuming that the edge length differences are minimized, centered at the origin, are given by all even permutations of:


 * (±1/2, ±c1, ±c2, ±c3)

where


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