Rectified octagonal duoprism

The rectified octagonal duoprism or reodip is a convex isogonal polychoron that consists of 16 rectified octagonal prisms and 64 tetragonal disphenoids. 3 rectified octagonal prisms and 2 tetragonal disphenoids join at each vertex. It can be formed by rectifying the octagonal duoprism.

It can also be formed as the convex hull of 2 oppositely oriented semi-uniform octagonal duoprisms, where the edges of one octagon are $$\sqrt{4-2\sqrt2} ≈ 1.08239$$ as long as the edges of the other.

The ratio between the longest and shortest edges is 1:$$\sqrt{\frac{2+\sqrt2}{2}}$$ ≈ 1:1.30656.

Vertex coordinates
The vertices of a rectified octagonal duoprism based on octagons of edge length 1, centered at the origin, are given by:


 * $$\left(±\frac12,\,±\frac{1+\sqrt2}{2},\,±\sqrt{\frac{2-\sqrt2}{2}},\,±\sqrt{\frac{2+\sqrt2}{2}}\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}{2},\,±\sqrt{\frac{2+\sqrt2}{2}},\,±\sqrt{\frac{2-\sqrt2}{2}}\right),$$
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,±\sqrt{\frac{2-\sqrt2}{2}},\,±\sqrt{\frac{2+\sqrt2}{2}}\right),$$
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,±\sqrt{\frac{2+\sqrt2}{2}},\,±\sqrt{\frac{2-\sqrt2}{2}}\right).$$
 * $$\left(±\sqrt2,\,0,\,±\sqrt{\frac{2+\sqrt2}{2}},\,0\right),$$
 * $$\left(±\sqrt2,\,0,\,0,\,±\sqrt{\frac{2+\sqrt2}{2}}\right),$$
 * $$\left(0,\,±\sqrt2,\,±\sqrt{\frac{2+\sqrt2}{2}},\,0\right),$$
 * $$\left(0,\,±\sqrt2,\,0,\,±\sqrt{\frac{2+\sqrt2}{2}}\right),$$
 * $$\left(±1,\,±1,\,±\sqrt{\frac{2+\sqrt2}{2}},\,0\right),$$
 * $$\left(±1,\,±1,\,0,\,±\sqrt{\frac{2+\sqrt2}{2}}\right),$$
 * $$\left(±\sqrt2,\,0,\,±\frac{\sqrt{2+\sqrt2}}{2},\,±\frac{\sqrt{2+\sqrt2}}{2}\right),$$
 * $$\left(0,\,±\sqrt2,\,±\frac{\sqrt{2+\sqrt2}}{2},\,±\frac{\sqrt{2+\sqrt2}}{2}\right),$$
 * $$\left(±1,\,±1,\,±\frac{\sqrt{2+\sqrt2}}{2},\,±\frac{\sqrt{2+\sqrt2}}{2}\right),$$