Bitetracontoctachoron

The bitetracontoctachoron or bicont, also known as the tetradisphenoidal diacosioctacontoctachoron or octafold octaswirlchoron, is a convex noble polychoron with 288 tetragonal disphenoids as cells. 24 cells join at each vertex, with the vertex figure being a triakis octahedron. It can be constructed as the convex hull of 2 dual icositetrachora.

It is the second in an infinite family of isogonal octahedral swirlchora (the octafold octaswirlchoron) and the first in an infinite family of isogonal chiral cuboctahedral swirlchora.

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

The tetragonal disphenoid cells of this polychoron are similar to those used as the vertex figure of the great tetracontoctachoron.

Vertex coordinates
Coordinates for the vertices of a bitetracontoctachoron of circumradius 1, centered at the origin, are given by all permutations of:
 * $$\left(±1,\,0,\,0,\,0\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac12,\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt2}{2},\,±\frac{\sqrt2}{2},\,0,\,0\right).$$

Variations
The bitetracontoctachoron has a number of isogonal or isotopic variations:


 * Disphenoidal diacosioctacontoctachoron (digonal disphenoid cells, isotopic)
 * Octafold octaswirlchoron (96 tetragonal and 192 phyllic disphenoids, swirlprism)

Isogonal derivatives
Substitution by vertices of these following elements will produce these convex isogonal polychora:
 * Tetragonal disphenoid (288): Tetracontoctachoron
 * Isosceles triangle (576): Rectified tetracontoctachoron
 * Edge (144): Small prismatotetracontoctachoron
 * Edge (192): Biambotetracontoctachoron