Triangular duotegum

The triangular duotegum or triddit, also known as the triangular-triangular duotegum, the 3 duotegum, or the 3-3 duotegum, is a noble duotegum that consists of 9 tetragonal disphenoids and 6 vertices, with 5 cells joining at a vertex. It is the simplest possible duotegum and it is also the 6-2 step prism. Together with its dual, it is the first in an infinite family of triangular dihedral swirlchora.

It shares the same vertex and edge configuration with the 5-dimensional hexateron. In fact, it is the simplest polytope that is not a simplex, but every pair of vertices is joined by an edge. Every n-2 step prism also has this property.

Vertex coordinates
The vertices of a triangular duotegum based on 2 unit-edge trianglese, centered at the origin, are given by:
 * $$\left(±\frac12, -\frac{\sqrt3}{6},\,0,\,0\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,0,\,0\right),$$
 * $$\left(0,\,0,\,±\frac12,\,-\frac{\sqrt3}{6}\right),$$
 * $$\left(0,\,0,\,0,\,\frac{\sqrt3}{3}\right).$$