Rectified decagonal duoprism

The rectified decagonal duoprism or rededip is a convex isogonal polychoron that consists of 20 rectified decagonal prisms and 100 tetragonal disphenoids. 3 rectified decagonal duoprisms and 2 tetragonal disphenoids join at each vertex. It can be formed by rectifying the decagonal duoprism.

It can also be formed as the convex hull of 2 oppositely oriented semi-uniform decagonal duoprisms, where the edges of one decagon are $$\sqrt{\frac{10-2\sqrt5}{5}} ≈ 1.05146$$ times as long as the edges of the other.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{5+\sqrt5}}{2}$$ ≈ 1:1.34500.

Vertex coordinates
The vertices of a rectified decagonal duoprism based on decagons of edge length 1, centered at the origin, are given by:
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,0,\,±\sqrt{\frac{10+2\sqrt5}{5}}\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,±1,\,±\sqrt{\frac{5+2\sqrt5}{5}}\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,±\frac{1+\sqrt5}{2},\,±\sqrt{\frac{5-\sqrt5}{10}}\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,0,\,±\sqrt{\frac{10+2\sqrt5}{5}}\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,±1,\,±\sqrt{\frac{5+2\sqrt5}{5}}\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\sqrt{\frac{5-\sqrt5}{10}}\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,0,\,±\sqrt{\frac{10+2\sqrt5}{5}}\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,±1,\,±\sqrt{\frac{5+2\sqrt5}{5}}\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,±\frac{1+\sqrt5}{2},\,±\sqrt{\frac{5-\sqrt5}{10}}\right),$$
 * $$\left(±\sqrt{\frac{10+2\sqrt5}{5}},\,0,\,±\frac{1+\sqrt5}{2},\,0\right),$$
 * $$\left(±\sqrt{\frac{10+2\sqrt5}{5}},\,0,\,±\frac{3+\sqrt5}{4},\,±\sqrt{\frac{5+\sqrt5}{8}}\right),$$
 * $$\left(±\sqrt{\frac{10+2\sqrt5}{5}},\,0,\,±\frac12,\,±\frac{\sqrt{5+2\sqrt5}}{2}\right),$$
 * $$\left(±\sqrt{\frac{5+2\sqrt5}{5}},\,±1,\,±\frac{1+\sqrt5}{2},\,0\right),$$
 * $$\left(±\sqrt{\frac{5+2\sqrt5}{5}},\,±1,\,±\frac{3+\sqrt5}{4},\,±\sqrt{\frac{5+\sqrt5}{8}}\right),$$
 * $$\left(±\sqrt{\frac{5+2\sqrt5}{5}},\,±1,\,±\frac12,\,±\frac{\sqrt{5+2\sqrt5}}{2}\right),$$
 * $$\left(±\sqrt{\frac{5-\sqrt5}{10}},\,±\frac{1+\sqrt5}{2},\,±\frac{1+\sqrt5}{2},\,0\right),$$
 * $$\left(±\sqrt{\frac{5-\sqrt5}{10}},\,±\frac{1+\sqrt5}{2},\,±\frac{3+\sqrt5}{4},\,±\sqrt{\frac{5+\sqrt5}{8}}\right),$$
 * $$\left(±\sqrt{\frac{5-\sqrt5}{10}},\,±\frac{1+\sqrt5}{2},\,±\frac12,\,±\frac{\sqrt{5+2\sqrt5}}{2}\right).$$