Triangular duoprism

The triangular duoprism or triddip, also known as the triangular-triangular duoprism, the 3 duoprism or the 3-3 duoprism, is a noble uniform duoprism that consists of 6 triangular prisms, with 4 meeting at each vertex. It is the simplest possible duoprism (excluding the degenerate dichora) and is also the 6-2 gyrochoron. It is the first in an infinite family of isogonal triangular dihedral swirlchora and also the first in an infinite family of isochoric triangular hosohedral swirlchora.

It is also a convex segmentochoron (designated K-4.10 on Richard Klitzing's list), as it is a triangle atop a triangular prism.

Vertex coordinates
Coordinates for the vertices of a triangular duoprism of edge length 1, centered at the origin, are given by:
 * $$\left(0,\,\frac{\sqrt3}{3},\,0,\,\frac{\sqrt3}{3}\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,±\frac12,\,-\frac{\sqrt3}{6}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,0,\,\frac{\sqrt3}{3}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12,\,-\frac{\sqrt3}{6}\right).$$

Representations
A triangular duoprism has the following Coxeter diagrams:


 * x3o x3o (full symmetry)
 * ox xx3oo&#x (axial, triangle atop triangular prism)
 * xxoo xoox&#xr (axial, vertex first)
 * xxx3ooo&#x (A2 axial)

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Triangular prism (6): Triangular duotegum
 * Triangle (6): Triangular duotegum
 * square (9): Triangular duoprism
 * Edge (18): Rectified triangular duoprism