Triangular duoantiprismatic antiprism

The triangular duoantiprismatic antiprism, or triddapap, is a convex isogonal polyteron that consists of 2 triangular duoantiprisms, 12 digonal-triangular duoantiprisms, and 36 tetragonal disphenoidal pyramids. 1 triangular duoantiprism, 4 digonal-triangular duoantiprisms, and 5 tetragonal disphenoidal pyramids join at each vertex. It can be obtained through the process of alternating the hexagonal duoprismatic prism. It cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt6}{2}$$ ≈ 1:1.22474.

Vertex coordinates
The vertices of a triangular duoantiprismatic antiprism, assuming that the edge length differences are minimized, centered at the origin, are given by:
 * $$\left(0,\,\frac{\sqrt3}{3},\,0,\,\frac{\sqrt3}{3},\,\frac{\sqrt6}{6}\right),$$
 * $$\left(0,\,-\frac{\sqrt3}{3},\,0,\,-\frac{\sqrt3}{3},\,\frac{\sqrt6}{6}\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,±\frac12,\,-\frac{\sqrt3}{6},\,\frac{\sqrt6}{6}\right),$$
 * $$\left(0,\,-\frac{\sqrt3}{3},\,±\frac12,\,\frac{\sqrt3}{6},\,\frac{\sqrt6}{6}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,0,\,\frac{\sqrt3}{3},\,\frac{\sqrt6}{6}\right),$$
 * $$\left(±\frac12,\,\frac{\sqrt3}{6},\,0,\,-\frac{\sqrt3}{3},\,\frac{\sqrt6}{6}\right),$$
 * $$\left(±\frac12,\,\frac{\sqrt3}{6},\,±\frac12,\,\frac{\sqrt3}{6},\,\frac{\sqrt6}{6}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12,\,-\frac{\sqrt3}{6},\,\frac{\sqrt6}{6}\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,0,\,-\frac{\sqrt3}{3},\,-\frac{\sqrt6}{6}\right),$$
 * $$\left(0,\,-\frac{\sqrt3}{3},\,0,\,\frac{\sqrt3}{3},\,-\frac{\sqrt6}{6}\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,±\frac12,\,\frac{\sqrt3}{6},\,-\frac{\sqrt6}{6}\right),$$
 * $$\left(0,\,-\frac{\sqrt3}{3},\,±\frac12,\,-\frac{\sqrt3}{6},\,-\frac{\sqrt6}{6}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,0,\,-\frac{\sqrt3}{3},\,-\frac{\sqrt6}{6}\right),$$
 * $$\left(±\frac12,\,\frac{\sqrt3}{6},\,0,\,\frac{\sqrt3}{3},\,-\frac{\sqrt6}{6}\right),$$
 * $$\left(±\frac12,\,\frac{\sqrt3}{6},\,±\frac12,\,-\frac{\sqrt3}{6},\,-\frac{\sqrt6}{6}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12,\,\frac{\sqrt3}{6},\,-\frac{\sqrt6}{6}\right).$$