Triangular-hexagonal duoantiprism

The triangular-hexagonal duoantiprism or thiddap, also known as the 3-6 duoantiprism, is a convex isogonal polychoron that consists of 6 hexagonal antiprisms, 12 triangular antiprisms, and 36 digonal disphenoids. 2 hexagonal antiprisms, 2 triangular antiprisms, and 4 digonal disphenoids join at each vertex. It can be obtained through the process of alternating the hexagonal-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:$$\frac{\sqrt{21+9\sqrt3}{22}}$$≈ 1:1.28962.

Vertex coordinates
The vertices of a triangular-hexagonal duoantiprism based on triangles and hexagons of edge length 1, centered at the origin, are given by:
 * $$\left(±1,\,0,\,0,\,\frac{\sqrt3}{3}\right),$$
 * $$\left(±1,\,0,\,±\frac12,\,-\frac{\sqrt3}{6}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt3}{2},\,0,\,\frac{\sqrt3}{3}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt3}{2},\,±\frac12,\,-\frac{\sqrt3}{6}\right),$$
 * $$\left(0,\,±1,\,0,\,-\frac{\sqrt3}{3}\right),$$
 * $$\left(0,\,±1,\,±\frac12,\,\frac{\sqrt3}{6}\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,0,\,-\frac{\sqrt3}{3}\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,±\frac12,\,\frac{\sqrt3}{6}\right).$$