Digonal double antiprismoid

The digonal double antiprismoid or didiap is a convex isogonal polychoron and the first member of the double antiprismoid family. It consists of 24 tetragonal disphenoids of two kinds and 32 sphenoids. 6 disphenoids and 8 sphenoids join at each vertex. It can be obtained as the convex hull of two orthogonal digonal-digonal duoantiprisms or by alternating the square ditetragoltriate. However, it cannot be made uniform. As such it is one of a number of polychora that can be obtained as the convex hull of two variant hexadecachora. It is the first in an infinite family of isogonal digonal antiprismatic swirlchora.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt{5+\sqrt5}}{2}$$ ≈ 1:1.34500. This variant is formed from duoantiprisms with base digons of length ratio 1:$$\frac{1+\sqrt5}{2}$$ ≈ 1:1.61803.

Vertex coordinates
The vertices of a digonal double antiprismoid, assuming that the two short edges have edge length 1, centered at the origin, are given by:
 * $$\left(0,\,±\frac12,\,0,\,±\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,0,\,±\frac{1+\sqrt5}{4},\,0\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{4},\,±\frac12,\,0\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,0,\,0,\,±\frac12\right).$$