Great transitional hexadecafold tetraantiprismatoswirlchoron

The great transitional hexadecafold tetraantiprismatoswirlchoron is an isogonal polychoron with 32 square gyroprisms, 128 mirror-symmetric notches, 128 rhombic disphenoids, 128 phyllic disphenoids, and 128 vertices. 2 square gyroprisms, 5 bilaterally-symmetric notches, 4 rhombic disphenoids, and 4 phyllic disphenoids join at each vertex. 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.

The ratio between the longest and shortest edges is 1:a ≈ 1:2.24110, where a is the largest positive real root of 1217a16-14888a14+69880a12-169568a10+235472a8-190976a6+86272a4-18432a2+1024.

Vertex coordinates
Coordinates for the vertices of a great transitional hexadecafold pentaantiprismatoswirlchoron, centered at the origin, are given by, along with their 90°, 180°, and 270° 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)),