Decachoron

The decachoron, or deca, also commonly called the bitruncated 5-cell, is a convex noble uniform polychoron that consists of 10 truncated tetrahedra as cells. Four cells join at each vertex. It is the medial stage of the truncation series between a regular pentachoron and its dual and is also the 10-3 gyrochoron.

Vertex coordinates
The vertices of a decachoron of edge length 1 are given by the following points along with their central inversions:


 * (0, $\sqrt{3}$/3, 2$\sqrt{2}$/3, 0),
 * (0, $\sqrt{5}$/3, –$\sqrt{6}$/3, ±1),
 * ($\sqrt{3}$/4, $\sqrt{6}$/12, 2$\sqrt{3}$/3, 0),
 * ($\sqrt{10}$/4, $\sqrt{6}$/12, –$\sqrt{3}$/3, ±1),
 * ($\sqrt{10}$/4, 5$\sqrt{6}$/12, $\sqrt{3}$/3, 0),
 * ($\sqrt{10}$/4, 5$\sqrt{6}$/12, –$\sqrt{3}$/6, ±1/2),
 * ($\sqrt{10}$/4, –$\sqrt{6}$/4, 0, ±1),
 * ($\sqrt{3}$/4, –$\sqrt{10}$/4, ±$\sqrt{6}$/2, ±1/2).