Bitetracontoctachoron

The bitetracontoctachoron or bicont, also known as the tetradisphenoidal diacosioctacontoctachoron, is a convex noble polychoron with 288 tetragonal disphenoids as cells. It is the second in an infinite family of isogonal octahedral swirlchora and the first in an infinite family of isogonal chiral cuboctahedral swirlchora.

It is also the convex hull of an icositetrachoron and its dual.

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

Vertex coordinates
Coordinates for the vertices of a bitetracontoctachoron of circumradius 1, centered at the origin, are given by all permutations and sign changes of:
 * (0, 0, 0, 1),
 * (1/2, 1/2, 1/2, 1/2),
 * (0, 0, $\sqrt{2}$/2, $\sqrt{2}$/2).

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