Hexagonal duoantiprism

The hexagonal duoantiprism or hiddap, also known as the hexagonal-hexagonal duoantiprism, the 6 duoantiprism or the 6-6 duoantiprism, is a convex isogonal polychoron that consists of 24 hexagonal antiprisms and 72 tetragonal disphenoids. 4 hexagonal antiprisms and 4 tetragonal disphenoids join at each vertex. It can be obtained through the process of alternating the dodecagonal duoprism. However, it cannot be made uniform, and has two edge lengths. It is the second in an infinite family of isogonal hexagonal dihedral swirlchora.

The ratio between the longest and shortest edges is 1:$$\frac{1+\sqrt3}{2}$$ ≈ 1:1.36603.

Vertex coordinates
The vertices of a hexagonal duoantiprism based on hexagons of edge length 1, centered at the origin, are give by:


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