Dodecagonal trioprism

The dodecagonal trioprism or twattip is a convex uniform trioprism that consists of 36 dodecagonal duoprismatic prisms as facets. 6 facets join at each vertex. It is also the 36-11-13 gyropeton.

This polypeton can be alternated into a hexagonal trioantiprism, although it cannot be made uniform. 12 of the dodecagons can also be alternated into long ditrigons to create a hexagonal duoprismatic-hexagonal prismantiprismoid, 144 of the dodecagonal prisms can also be edge-alternated to create a hexagonal prismatic-hexagonal prismatic prismantiprismoid and 24 of the dodecagonal duoprisms can also be edge-alternated to create a hexagonal-hexagonal duoprismatic prismantiprismoid, which are nonuniform.

Vertex coordinates
The vertices of a dodecagonal trioprism of edge length 1 are given by:
 * $$\left(±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2}\right),$$
 * $$\left(±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac12,\,±\frac{2+\sqrt3}{2}\right),$$
 * $$\left(±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{2+\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2}\right),$$
 * $$\left(±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac{2+\sqrt3}{2}\right),$$
 * $$\left(±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac{2+\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2}\right),$$
 * $$\left(±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac12,\,±\frac{2+\sqrt3}{2}\right),$$
 * $$\left(±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac12,\,±\frac{2+\sqrt3}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{2+\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac{2+\sqrt3}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac{2+\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac12,\,±\frac{2+\sqrt3}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2}\right),$$
 * $$\left(±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac12,\,±\frac{2+\sqrt3}{2}\right),$$
 * $$\left(±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{2+\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2}\right),$$
 * $$\left(±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac{2+\sqrt3}{2}\right),$$
 * $$\left(±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac{2+\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2}\right),$$
 * $$\left(±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac12,\,±\frac{2+\sqrt3}{2}\right),$$
 * $$\left(±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac12\right).$$