Rectified dodecagonal duoprism

The rectified dodecagonal duoprism or retwadip is a convex isogonal polychoron that consists of 24 rectified dodecagonal prisms and 144 tetragonal disphenoids. 3 rectified dodecagonal prisms and 2 tetragonal disphenoids join at each vertex. It can be formed by rectifying the dodecagonal duoprism.

It can also be formed as the convex hull of 2 oppositely oriented semi-uniform dodecagonal duoprisms, where the edges of one dodecagon are $$\sqrt6-\sqrt2 ≈ 1.03528$$ times as long as the edges of the other.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{1+\sqrt3}{2}$$ ≈ 1:1.36603.

Vertex coordinates
The vertices of a rectified dodecagonal duoprism based on dodecagons of edge length 1, centered at the origin, are given by:
 * $$\left(±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\sqrt2,\,±\sqrt2\right),$$
 * $$\left(±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{\sqrt6-\sqrt2}{2},\,±\frac{\sqrt2+\sqrt6}{2}\right),$$
 * $$\left(±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2},\,±\frac{\sqrt2+\sqrt6}{2},\,±\frac{\sqrt6-\sqrt2}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}{2},\,±\sqrt2,\,±\sqrt2\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac{\sqrt6-\sqrt2}{2},\,±\frac{\sqrt2+\sqrt6}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}{2},\,±\frac{\sqrt2+\sqrt6}{2},\,±\frac{\sqrt6-\sqrt2}{2}\right),$$
 * $$\left(±\frac{2+\sqrt3}{2},\,±\frac12,\,±\sqrt2,\,±\sqrt2\right),$$
 * $$\left(±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac{\sqrt6-\sqrt2}{2},\,±\frac{\sqrt2+\sqrt6}{2}\right),$$
 * $$\left(±\frac{2+\sqrt3}{2},\,±\frac12,\,±\frac{\sqrt2+\sqrt6}{2},\,±\frac{\sqrt6-\sqrt2}{2}\right),$$
 * $$\left(±2,\,0,\,±\frac{\sqrt2+\sqrt6},\,0\right),$$
 * $$\left(±2,\,0,\,0,\,±\frac{\sqrt2+\sqrt6}{2}\right),$$
 * $$\left(0,\,±2,\,±\frac{\sqrt2+\sqrt6},\,0\right),$$
 * $$\left(0,\,±2,\,0,\,±\frac{\sqrt2+\sqrt6}{2}\right),$$
 * $$\left(±2,\,0,\,±\frac{\sqrt2+\sqrt6}{4},\,±\frac{3\sqrt2+\sqrt6}{4}\right),$$
 * $$\left(0,\,±2,\,±\frac{\sqrt2+\sqrt6}{4},\,±\frac{3\sqrt2+\sqrt6}{4}\right),$$
 * $$\left(±2,\,0,\,±\frac{3\sqrt2+\sqrt6}{4},\,±\frac{\sqrt2+\sqrt6}{4}\right),$$
 * $$\left(0,\,±2,\,±\frac{3\sqrt2+\sqrt6}{4},\,±\frac{\sqrt2+\sqrt6}{4}\right),$$
 * $$\left(±\sqrt3,\,±1,\,±\frac{\sqrt2+\sqrt6},\,0\right),$$
 * $$\left(±\sqrt3,\,±1,\,0,\,±\frac{\sqrt2+\sqrt6}{2}\right),$$
 * $$\left(±1,\,±\sqrt3,\,±\frac{\sqrt2+\sqrt6},\,0\right),$$
 * $$\left(±1,\,±\sqrt3,\,0,\,±\frac{\sqrt2+\sqrt6}{2}\right),$$
 * $$\left(±\sqrt3,\,±1,\,±\frac{\sqrt2+\sqrt6}{4},\,±\frac{3\sqrt2+\sqrt6}{4}\right),$$
 * $$\left(±1,\,±\sqrt3,\,±\frac{\sqrt2+\sqrt6}{4},\,±\frac{3\sqrt2+\sqrt6}{4}\right),$$
 * $$\left(±\sqrt3,\,±1,\,±\frac{3\sqrt2+\sqrt6}{4},\,±\frac{\sqrt2+\sqrt6}{4}\right),$$
 * $$\left(±1,\,±\sqrt3,\,±\frac{3\sqrt2+\sqrt6}{4},\,±\frac{\sqrt2+\sqrt6}{4}\right),$$