Digonal-hexagonal prismantiprismoid

The digonal-hexagonal prismantiprismoid or dihipap, also known as the edge-snub digonal-hexagonal duoprism or 2-6 prismantiprismoid, is a convex isogonal polychoron that consists of 4 ditrigonal trapezoprisms, 6 tetragonal disphenoids, and 12 wedges. 1 tetragonal disphenoid, 2 ditrigonal trapezoprisms, and 3 wedges join at each vertex. It can be obtained through the process of alternating one class of edges of the square-dodecagonal duoprism so that the dodecagons become ditrigons. However, it cannot be made uniform, as it generally has 4 edge lengths, which can be minimized to no fewer than 2 different sizes.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{2+2\sqrt6}{5}$$ ≈ 1:1.37980.

Vertex coordinates
The vertices of a digonal-hexagonal prismantiprismoid based on a square-dodecagonal duoprism of edge length 1, centered at the origin, are given by:


 * $$\left(0,\,±\frac{\sqrt2}{2},\,±\frac12,\,\frac{2+\sqrt3}{2}\right),$$
 * $$\left(0,\,±\frac{\sqrt2}{2},\,±\frac{2+\sqrt3}{2},\,-\frac12\right),$$
 * $$\left(0,\,±\frac{\sqrt2}{2},\,±\frac{1+\sqrt3}{2},\,-\frac{1+\sqrt3}{2}\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,0,\,±\frac12,\,-\frac{2+\sqrt3}{2}\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,0,\,±\frac{2+\sqrt3}{2},\,\frac12\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,0,\,±\frac{1+\sqrt3}{2},\,\frac{1+\sqrt3}{2}\right).$$

An alternate set of coordinates, assuming that the edge length differences are minimized, centered at the origin, are given by:


 * $$\left(±\frac{\sqrt6-1}{4},\,\frac{\sqrt2+\sqrt3}{4},\,±\frac12,\,0\right),$$
 * $$\left(±\frac{1+\sqrt6}{4},\,-\frac{\sqrt3-\sqrt2}{4},\,±\frac12,\,0\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt2}{2},\,±\frac12,\,0\right),$$
 * $$\left(±\frac{\sqrt6-1}{4},\,-\frac{\sqrt2+\sqrt3}{4},\,0,\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt6}{4},\,\frac{\sqrt3-\sqrt2}{4},\,0,\,±\frac12\right),$$
 * $$\left(±\frac12,\,\frac{\sqrt2}{2},\,0,\,±\frac12\right).$$