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.

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).

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Truncated cube (48): Bitetracontoctachoron
 * Triangle (192): Biambotetracontoctachoron
 * Octagon (144): Small prismatotetracontoctachoron
 * Edge (576): Rectified tetracontoctachoron

Representations
A tetracontoctachoron has the following Coxeter diagrams:


 * o3x4x3o (full symmetry)
 * xo4xw3oo3wx&#zx (BC4 symmetry)
 * xooxwUwxoox4xwwxoooxwwx3ooxwwxwwxoo&#xt (BC3 axial, cell-first)