Top dense hyperbolic ball packings and coverings for complete Coxeter orthoscheme groups

Emil Molnár, Jenő Szirmai

In $n$-dimensional hyperbolic space ${\mathbf{H}}^n$ $(n\ge 2)$ there are $3$-types of spheres (balls): the sphere, horosphere and hypersphere. If $n=2,3$ we know an universal upper b…