Dodecagonal trioprism

The dodecagonal trioprism or twattip is a convex uniform trioprism that consists of 36 dodecagonal duoprismatic prisms. 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:
 * (±(1+$\sqrt{6+3√3}$)/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2),
 * (±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±1/2, ±(2+$\sqrt{3}$)/2),
 * (±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(2+$\sqrt{3}$)/2, ±1/2),
 * (±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±1/2, ±(2+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2),
 * (±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±1/2, ±(2+$\sqrt{3}$)/2, ±1/2, ±(2+$\sqrt{3}$)/2),
 * (±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±1/2, ±(2+$\sqrt{3}$)/2, ±(2+$\sqrt{3}$)/2, ±1/2),
 * (±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(2+$\sqrt{3}$)/2, ±1/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2),
 * (±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(2+$\sqrt{3}$)/2, ±1/2, ±1/2, ±(2+$\sqrt{3}$)/2),
 * (±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(2+$\sqrt{3}$)/2, ±1/2, ±(2+$\sqrt{3}$)/2, ±1/2),
 * (±1/2, ±(2+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2),
 * (±1/2, ±(2+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±1/2, ±(2+$\sqrt{3}$)/2),
 * (±1/2, ±(2+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(2+$\sqrt{3}$)/2, ±1/2),
 * (±1/2, ±(2+$\sqrt{3}$)/2, ±1/2, ±(2+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2),
 * (±1/2, ±(2+$\sqrt{3}$)/2, ±1/2, ±(2+$\sqrt{3}$)/2, ±1/2, ±(2+$\sqrt{3}$)/2),
 * (±1/2, ±(2+$\sqrt{3}$)/2, ±1/2, ±(2+$\sqrt{3}$)/2, ±(2+$\sqrt{3}$)/2, ±1/2),
 * (±1/2, ±(2+$\sqrt{3}$)/2, ±(2+$\sqrt{3}$)/2, ±1/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2),
 * (±1/2, ±(2+$\sqrt{3}$)/2, ±(2+$\sqrt{3}$)/2, ±1/2, ±1/2, ±(2+$\sqrt{3}$)/2),
 * (±1/2, ±(2+$\sqrt{3}$)/2, ±(2+$\sqrt{3}$)/2, ±1/2, ±(2+$\sqrt{3}$)/2, ±1/2),
 * (±(2+$\sqrt{3}$)/2, ±1/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2),
 * (±(2+$\sqrt{3}$)/2, ±1/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±1/2, ±(2+$\sqrt{3}$)/2),
 * (±(2+$\sqrt{3}$)/2, ±1/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(2+$\sqrt{3}$)/2, ±1/2),
 * (±(2+$\sqrt{3}$)/2, ±1/2, ±1/2, ±(2+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2),
 * (±(2+$\sqrt{3}$)/2, ±1/2, ±1/2, ±(2+$\sqrt{3}$)/2, ±1/2, ±(2+$\sqrt{3}$)/2),
 * (±(2+$\sqrt{3}$)/2, ±1/2, ±1/2, ±(2+$\sqrt{3}$)/2, ±(2+$\sqrt{3}$)/2, ±1/2),
 * (±(2+$\sqrt{3}$)/2, ±1/2, ±(2+$\sqrt{3}$)/2, ±1/2, ±(1+$\sqrt{3}$)/2, ±(1+$\sqrt{3}$)/2),
 * (±(2+$\sqrt{3}$)/2, ±1/2, ±(2+$\sqrt{3}$)/2, ±1/2, ±1/2, ±(2+$\sqrt{3}$)/2),
 * (±(2+$\sqrt{3}$)/2, ±1/2, ±(2+$\sqrt{3}$)/2, ±1/2, ±(2+$\sqrt{3}$)/2, ±1/2).