Digonal double prismantiprismoid

The digonal double prismantiprismoid is a convex isogonal polychoron and the first member of the double prismantiprismoid family. It consists of 16 wedges, 32 isosceles trapezoidal pyramids, 8 tetragonal disphenoids, and 16 digonal disphenoids. 3 wedges, 5 isosceles trapezoidal pyramids, 1 tetragonal disphenoid, and 2 digonal disphenoids join at each vertex. It can be obtained as the convex hull of two orthogonal digonal-square prismantiprismoids. However, it cannot be made scaliform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:a ≈ 1:1.12130, where a is the largest real root of 5x4+4x3-10x2-8x+8.

Vertex coordinates
The vertices of an optimized digonal double prismantiprismoid using the ratio method, centered at the origin, are given by all cyclic permutations of:
 * $$\left(0,\,±\frac12,\,±c_1,\,±c_2\right),$$

where


 * $$c_1=\text{root}(10x^4+4x^3-5x^2-2x+1, 2) ≈ 0.5606517483597204049669253,$$
 * $$c_2=\text{root}(80x^4-64x^3-8x-1, 2) ≈ 0.9308939742688318775680784,$$