Hexagonal trioprism

The hexagonal trioprism or hittip is a convex uniform trioprism that consists of 18 hexagonal duoprismatic prisms as facets. 6 facets join at each vertex. It is also the 18-5-7 gyropeton.

This polypeton can be alternated into a triangular trioantiprism, although it cannot be made uniform.

The hexagonal trioprism can be vertex-inscribed into the rectified pentacontatetrapeton.

Vertex coordinates
The vertices of a hexagonal trioprism of edge length 1 are given by:
 * $$\left(0,\,±1,\,0,\,±1,\,0,\,±1\right),$$
 * $$\left(0,\,±1,\,0,\,±1,\,±\frac{\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(0,\,±1,\,±\frac{\sqr23}{2},\,±\frac12,\,0,\,±1\right),$$
 * $$\left(0,\,±1,\,±\frac{\sqrt3}{2},\,±\frac12,\,±\frac{\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,0,\,±1,\,0,\,±1\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,0,\,±1,\,±\frac{\sqrt3}{2},\,±\rac12\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,±\frac{\sqrt3}{2},\,±\frac12,\,0,\,±1\right),$$
 * $$\left(±\frac{\sqrt3}{2},\,±\frac12,\,±\frac{\sqrt3}{2},\,±\frac12,\,±\frac{\sqrt3}{2},\,±\frac12\right).$$