Biprismatododecateron

The biprismatododecateron, or bad, is a uniform polyteron. It consists of 12 faceted rectified pentachora and 20 triangular duoprisms. 6 faceted rectified pentachora and 9 triangular duoprisms join at each vertex.

Vertex coordinates
The vertices of a dodecateron of edge length 1 are given by the following points, the same as a dodecateron:


 * $$±\left(\frac{\sqrt{15}}{10},\,-\frac{3\sqrt{10}}{20},\,-\frac{\sqrt6}{4},\,0,\,0\right),$$
 * $$±\left(\frac{\sqrt{15}}{10},\,-\frac{3\sqrt{10}}{20},\,\frac{\sqrt6}{12},\,-\frac{\sqrt3}{3},\,0\right),$$
 * $$±\left(-\frac{\sqrt{15}}{10},\,-\frac{3\sqrt{10}}{20},\,\frac{\sqrt6}{12},\,\frac{\sqrt3}{6},\,±\frac12\right),$$
 * $$±\left(\frac{\sqrt{15}}{10},\,\frac{\sqrt{10}}{10},\,\frac{\sqrt6}{6},\,\frac{\sqrt3}{3},\,0\right),$$
 * $$±\left(\frac{\sqrt{15}}{10},\,\frac{\sqrt{10}}{10},\,-\frac{\sqrt6}{6},\,-\frac{\sqrt3}{3},\,0\right),$$
 * $$±\left(\frac{\sqrt{15}}{10},\,\frac{\sqrt{10}}{10},\,\frac{\sqrt6}{6},\,-\frac{\sqrt3}{6},\,±\frac12\right),$$
 * $$\left(\frac{\sqrt{15}}{10},\,\frac{\sqrt{10}}{10},\,-\frac{\sqrt6}{6},\,\frac{\sqrt3}{6},\,±\frac12\right).$$

Much simpler coordinates can be given in six dimensions, as all permutations of:


 * $$\left(\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,\frac{\sqrt2}{2},\,0,\,0,\,0\right).$$