Difold ditetraswirlchoron

The difold ditetraswirlchoron, also known as the disphenoidal-digonal scalenohedral 8-3 double step prism, is one of several isogonal polychoron, formed as a convex hull of two hexadecachora. It consists of 8 triangular gyroprisms, 16 triangular pyramids, and 24 phyllic disphenoids. 3 triangular gyroprisms, 4 triangular pyramids, and 6 phyllic disphenoids join at each vertex.

This polychoron cannot be optimized using the ratio method, because the solution (with intended minimal ratio 1:$$\sqrt2$$ ≈ 1:1.41421) would yield a tesseract instead.

Vertex coordinates
Coordinates for the vertices of a difold ditetraswirlchoron based on a 2D regular dodecagonal envelope of circumradius 1, centered at the origin, are given by:
 * $$±\left(0,\,0,\,0,\,1\right),$$
 * $$±\left(\frac{\sqrt6}{3},\,0,\,\frac{\sqrt3}{3},\,0\right),$$
 * $$±\left(\frac{\sqrt6}{6},\,±\frac{\sqrt2}{2},\,-\frac{\sqrt3}{3},\,0\right),$$
 * $$±\left(0,\,0,\,\frac12,\,\frac{\sqrt3}{2}\right),$$
 * $$±\left(0,\,\frac{\sqrt6}{3},\,-\frac12,\,\frac{\sqrt3}{6}\right),$$
 * $$±\left(±\frac{\sqrt2}{2},\,\frac{\sqrt6}{3},\,\frac12,\,-\frac{\sqrt3}{6}\right).$$