Difold ditetraswirlchoron

The difold ditetraswirlchoron, also known as the disphenoidal-digonal scalenohedral 8-3 double step prism, is a convex isogonal polychoron, formed as a convex hull of two hexadecachora. It consists of 8 triangular antiprisms, 16 triangular pyramids and 24 phyllic disphenoids.

This polychoron cannot be optimized using the ratio method, because the solution (with intended minimal ratio 1:$\sqrt{2}$) would yield a tesseract instead.

Vertex coordinates
Coordinates for the vertices of a difold ditetraswirlchoron of circumradius 1, centered at the origin, are given by:
 * ±(0, 0, 0, 1),
 * ±($\sqrt{6}$/3, 0, $\sqrt{3}$/3, 0),
 * ±($\sqrt{6}$/6, ±$\sqrt{2}$/2, -$\sqrt{3}$/3, 0),
 * ±(0, 0, 1/2, $\sqrt{3}$/2),
 * ±(0, $\sqrt{6}$/3, -1/2, $\sqrt{3}$/6),
 * ±(±$\sqrt{2}$/2, $\sqrt{6}$/3, 1/2, -$\sqrt{3}$/6).