Tetracontoctachoron

The tetracontoctachoron, or cont, also commonly called the bitruncated 24-cell, is a convex noble uniform polychoron that consists of 48 truncated cubes as cells. Four cells join at each vertex. It is the medial stage of the truncation series between a regular icositetrachoron and its dual. Together with its dual, it is the second in a series of cubic swirlchora (the first is the icositetrachoron and the third is a polychoron with 72 identical chiral square antiprisms).

Vertex coordinates
The vertices of a tetracontoctachoron of edge length 1 are all permutations of:


 * (±(1+$\sqrt{2+√2}$), ±(2+$\sqrt{2}$)/2, ±(2+$\sqrt{2}$)/2, 0),
 * (±(3+2$\sqrt{2}$)/2, ±(1+$\sqrt{2}$)/2, ±(1+$\sqrt{2}$)/2, ±1/2).