Pyritosnub tesseract

The bialternatosnub 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 bialternating (i.e. alternating two adjacent vertices) the great disprismatotesseractihexadecachoron. However, it cannot be made uniform.

A variant with regular icosahedra can be vertex-inscribed into a prismatorhombisnub icositetrachoron.

Vertex coordinates
The vertices of a bialternatosnub hexadecachoron, 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).