Leech polytope

The Leech polytope, or leech, is a convex isogonal polyiktron with 1197362269604214277200 iktra, 5081469120 edges and 196560 vertices. It is the contact polytope of the Leech lattice, which represents a symmetric packing of 196560 non-overlapping 23-spheres that touch each other around a common 23-sphere.

The Leech polytope is chiral, and has a lower symmetry order than the 3 regular polyiktra.

The ratio between the longest and shortest edges is $$\frac{\sqrt6}{2}$$ ≈ 1.22474.