Decafold tetraswirlchoron

The decafold tetraswirlchoron is an isogonal polychoron with 240 phyllic disphenoids of two types and 40 vertices. 12 of each facet type join at each vertex. It is the fifth in an infinite family of isogonal tetrahedral swirlchora.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{27+9\sqrt5-3\sqrt{15+6\sqrt5}}}{3}$$ ≈ 1:1.85988.

Vertex coordinates
Coordinates for the vertices of a decafold tetraswirlchoron of circumradius 1, centered at the origin, are given by: along with 120° and 240° rotations in the xy axis of: where k is an integer from 0 to 4.
 * ±(0, 0, sin(kπ/5), cos(kπ/5)),
 * ±($\sqrt{6}$sin(kπ/5)/3, $\sqrt{6}$cos(kπ/5)/3, $\sqrt{3}$cos(kπ/5)/3, $\sqrt{3}$sin(kπ/5)/3),

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Edge (40): Decafold tetraswirlchoron
 * Edge (120): Small decafold truncatotetraswirlchoron
 * Edge (120): Great decafold truncatotetraswirlchoron