Icosafold ambotetraswirlchoron

The icosafold ambotetraswirlchoron is an isogonal polychoron with 80 triangular gyroprisms, 480 phyllic disphenoids of two kinds, and 120 vertices. 4 triangular gyoprisms and 16 phyllic disphenoids join at each vertex. It is the fifth in an infinite family of isogonal ambotetrahedral swirlchora.

The ratio between the longest and shortest edges is 1:$$\sqrt{\frac{\sqrt3+\sqrt5+\sqrt{15}+(\sqrt3-1)\sqrt{10-2\sqrt5}-15}{4\sqrt{10+2\sqrt5}-16}}$$ ≈ 1:2.63513.

Vertex coordinates
Coordinates for the vertices of an icosafold ambotetraswirlchoron of circumradius 1, centered at the origin, are given by, along with their 120° and 240° rotations in the xy axis of: where k is an integer from 0 to 9.
 * ±(sin(kπ/10)/$\sqrt{3+√3}$, cos(kπ/10)/$\sqrt{3+√3}$, cos(kπ/10)/$\sqrt{3-√3}$, sin(kπ/10)/$\sqrt{3-√3}$),
 * ±(sin((k+1)π/10)/$\sqrt{3-√3}$, cos((k+1)π/10)/$\sqrt{3-√3}$, -cos((k+1)π/10)/$\sqrt{3+√3}$, -sin((k+1)π/10)/$\sqrt{3+√3}$),