Digonal-hexagonal triprismantiprismoid

The digonal-hexagonal triprismantiprismoid is a convex isogonal polychoron that consists of 6 rectangular gyroprisms, 12 digonal-rectangular gyrowedges, 6 rhombic disphenoids, and 12 phyllic disphenoids. 2 rectangular gyroprism, 2 rhombic disphenoids, and 4 phyllic disphenoids join at each vertex. It can be obtained as a subsymmetrical faceting of the hexagonal-dihexagonal duoprism. However, it cannot be made scaliform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt{8+2\sqrt{15}}}{2}$$ ≈ 1:1.98406.

Vertex coordinates
The vertices of a digonal-hexagonal triprismantiprismoid, assuming that the edge length differences are minimized, using the ratio method, are given by all even permutations of the first two coordinates of:
 * $$±\left(\frac12,\,\frac{\sqrt3+\sqrt5}{4},\,0,\,\frac{\sqrt3+\sqrt5}{4}\right),$$
 * $$±\left(\frac12,\,-\frac{\sqrt3+\sqrt5}{4},\,0,\,\frac{\sqrt3+\sqrt5}{4}\right),$$
 * $$±\left(\frac{1+\sqrt{15}}{8},\,\frac{3\sqrt3+\sqrt5}{8},\,\frac{3+\sqrt{15}}{8},\,\frac{\sqrt3+\sqrt5}{8}\right),$$
 * $$±\left(\frac{5+\sqrt{15}}{8},\,\frac{\sqrt5-\sqrt3}{8},\,\frac{3+\sqrt{15}}{8},\,\frac{\sqrt3+\sqrt5}{8}\right),$$
 * $$±\left(\frac{5+\sqrt{15}}{8},\,\frac{\sqrt3-\sqrt5}{8},\,\frac{3+\sqrt{15}}{8},\,-\frac{\sqrt3+\sqrt5}{8}\right),$$
 * $$±\left(\frac{1+\sqrt{15}}{8},\,-\frac{3\sqrt3+\sqrt5}{8},\,\frac{3+\sqrt{15}}{8},\,-\frac{\sqrt3+\sqrt5}{8}\right).$$