Digonal-hexagonal duoantiprism

The digonal-hexagonal duoantiprism or dihidap, also known as the 2-6 duoantiprism, is a convex isogonal polychoron that consists of 4 hexagonal antiprisms, 12 tetragonal disphenoids, and 24 digonal disphenoids. 2 hexagonal antiprisms, 2 tetragonal disphenoids, and 4 digonal disphenoids join at each vertex. It can be obtained through the process of alternating the square-dodecagonal duoprism. However, it cannot be made uniform, as it generally has 3 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:$$\sqrt{\frac{10+4\sqrt3}{13}}$$ ≈ 1:1.14113.

Vertex coordinates
The vertices of a digonal-hexagonal duoantiprism, assuming that the hexagonal antiprisms are uniform of edge length 1, centered at the origin, are given by:
 * $$\left(0,\,±1,\,\sqrt{\frac{\sqrt3-1}{2}},\,\sqrt{\frac{\sqrt3-1}{2}}\right),$$
 * $$\left(0,\,±1,\,-\sqrt{\frac{\sqrt3-1}{2}},\,-\sqrt{\frac{\sqrt3-1}{2}}\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,\sqrt{\frac{\sqrt3-1}{2}},\,\sqrt{\frac{\sqrt3-1}{2}}\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,-\sqrt{\frac{\sqrt3-1}{2}},\,-\sqrt{\frac{\sqrt3-1}{2}}\right),$$
 * $$\left(±1,\,0,\,\sqrt{\frac{\sqrt3-1}{2}},\,-\sqrt{\frac{\sqrt3-1}{2}}\right),$$
 * $$\left(±1,\,0,\,-\sqrt{\frac{\sqrt3-1}{2}},\,\sqrt{\frac{\sqrt3-1}{2}}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt3}{2},\,\sqrt{\frac{\sqrt3-1}{2}},\,-\sqrt{\frac{\sqrt3-1}{2}}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt3}{2},\,-\sqrt{\frac{\sqrt3-1}{2}},\,\sqrt{\frac{\sqrt3-1}{2}}\right).$$

An alternate set of coordinates, assuming that the edge length differences are minimized, centered at the origin, are given by:
 * $$\left(0,\,±1,\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right),$$
 * $$\left(0,\,±1,\,-\frac{\sqrt2}{4},\,-\frac{\sqrt2}{4}\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,-\frac{\sqrt2}{4},\,-\frac{\sqrt2}{4}\right),$$
 * $$\left(±1,\,0,\,\frac{\sqrt2}{4},\,-\frac{\sqrt2}{4}\right),$$
 * $$\left(±1,\,0,\,-\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt3}{2},\,\frac{\sqrt2}{4},\,-\frac{\sqrt2}{4}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt3}{2},\,-\frac{\sqrt2}{4},\,\frac{\sqrt2}{4}\right).$$