Triangular trioprism

The triangular trioprism or trittip is a convex uniform trioprism that consists of 9 triangular duoprismatic prisms as facets. 6 facets join at each vertex. It is the simplest possible trioprism. It is also the 9-2-4 gyropeton.

The triangular trioprism can be edge-inscribed into a pentacontatetrapeton. It is also related to the scaliform octadecadiminished pentacontatetrapeton, which is the convex hull of two tri-orthogonal triangular trioprisms.

The triangular trioprism contains the real embedding of the 3-generalized 3-cube as a complex polyhedron, and in the projection they have the same edge arrangement.

Vertex coordinates
The vertices of a triangular trioprism of edge length 1 are given by:
 * $$\left(0,\,\frac{\sqrt3}{3},\,0,\,\frac{\sqrt3}{3},\,0,\,\frac{\sqrt3}{3}\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,0,\,\frac{\sqrt3}{3},\,±\frac12,\,-\frac{\sqrt3}{6}\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,±\frac12,\,-\frac{\sqrt3}{6},\,0,\,\frac{\sqrt3}{3}\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12,\,-\frac{\sqrt3}{6}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,0,\,\frac{\sqrt3}{3},\,0,\,\frac{\sqrt3}{3}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,0,\,\frac{\sqrt3}{3}\,±\frac12,\,-\frac{\sqrt3}{6}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12,\,-\frac{\sqrt3}{6},\,0,\,\frac{\sqrt3}{3}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12,\,-\frac{\sqrt3}{6}\right).$$