Rectified triangular duoprism

The rectified triangular duoprism or retdip is a convex isogonal polychoron that consists of 6 rectified triangular prisms and 9 tetragonal disphenoids. 3 rectified triangular prisms and 2 tetragonal disphenoids join at each vertex. It can be formed by rectifying the triangular duoprism.

It can also be formed as the convex hull of 2 oppositely oriented semi-uniform triangular duoprisms, where the edges of one triangle are exactly twice as long as the edges of the other.

The ratio between the longest and shortest edges is 1:$$\sqrt2$$ ≈ 1:1.41421.

Vertex coordinates
Coordinates for the vertices of a rectified triangular duoprism based on equilateral triangles of edge length 1, centered at the origin, are given by:
 * $$\left(0,\,\frac{\sqrt3}{3},\,0,\,\frac{2\sqrt3}{3}\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,±1,\,-\frac{\sqrt3}{3}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,0,\,\frac{2\sqrt3}{3}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,±1,\,-\frac{\sqrt3}{3}\right).$$
 * $$\left(0,\,-\frac{2\sqrt3}{3},\,0,\,-\frac{\sqrt3}{3}\right),$$
 * $$\left(0,\,-\frac{2\sqrt3}{3},\,±\frac12,\,\frac{\sqrt3}{6}\right),$$
 * $$\left(±1,\,\frac{\sqrt3}{3},\,0,\,-\frac{\sqrt3}{3}\right),$$
 * $$\left(±1,\,\frac{\sqrt3}{3},\,±\frac12,\,\frac{\sqrt3}{6}\right).$$

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Rectified triangular prism (6): Triangular duotegum
 * Tetragonal disphenoid (9): Triangular duoprism
 * Triangle (6): Triangular duotegum
 * Square (9): Triangular duoprism
 * Isosceles triangle (36): Triangular duoexpandoprism
 * Edge (18): Rectified triangular duoprism
 * Edge (36): Semi-uniform hexagonal duoprism