Great transitional hexadecafold tetraantiprismatoswirlchoron

The great transitional hexadecafold tetraantiprismatoswirlchoron is an isogonal polychoron with 32 square antiprisms, 128 mirror-symmetric notches, 256 phyllic disphenoids of two kinds and 128 vertices. It is the second in an infinite family of isogonal square antiprismatic swirlchora, the others being the small hexadecafold tetraantiprismatoswirlchoron, great hexadecafold tetraantiprismatoswirlchoron and small transitional hexadecafold tetraantiprismatoswirlchoron.

Vertex coordinates
Coordinates for the vertices of a great transitional hexadecafold pentaantiprismatoswirlchoron, centered at the origin, are given by, along with their 72°, 144°, 216° and 288° rotations in the xy axis of: where b/a = (2+$\sqrt{2}$+2$\sqrt{2+√2}$+$\sqrt{8√2-2-4√4-2√2}$)/4 and k is an integer from 0 to 7.
 * ±(a*sin(kπ/8), a*cos(kπ/8), b*cos(kπ/8), b*sin(kπ/8)),
 * ±(b*sin((k+2)π/8), b*cos((k+2)π/8), a*cos(kπ/8), a*sin(kπ/8)),