Great icosafold pentaantiprismatoswirlchoron

The icosafold pentaantiprismatoswirlchoron is an isogonal polychoron with 40 pentagonal gyroprisms, 600 phyllic disphenoids of three kinds, 400 irregular tetrahedra, and 200 vertices. 2 pentagonal gyroprisms, 12 phyllic disphenoids, and 8 rregular tetrahedra join at each vertex. It is the second in an infinite family of isogonal pentagonal antiprismatic swirlchora.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt{8+2\sqrt{10+2\sqrt5}}}{2}$$ ≈ 1:1.97538.

Vertex coordinates
Coordinates for the vertices of an icosafold pentaantiprismatoswirlchoron, centered at the origin, are given by, along with their 72°, 144°, 216° and 288° rotations in the xy axis of: where a = $\sqrt{50+10√5}$/10, b = $\sqrt{25+10√5}$/5 and k is an integer from 0 to 9.
 * ±(a*sin(kπ/10), a*cos(kπ/10), b*cos(kπ/10), b*sin(kπ/10)),
 * ±(b*sin((k+2)π/10), b*cos((k+2)π/10), a*cos(kπ/10), a*sin(kπ/10)),