OPTIMAL PACKING OF UNIT MINKOWSKI SPHERES ON A PLANE

The optimal packing of unit Minkowski spheres on a plane has been studied. The moduli space (parameterization) of admissible lattices of doubled Minkowski spheres, which contain three pairs of points on the corresponding Minkowski sphere, and which determine the packing lattices of unit Minkowski spheres, is constructed. According to the results of the proof of Minkowski’s hypothesis about the critical determinant, a partition of Minkowski spheres into 3 classes was obtained: Watson spheres, Davis spheres, and Mordell–Chebyshev spheres. Lattices that give optimal packings of these spheres are indicated, and densities of these optimal packings are found. Keywords: Minkowski sphere, admissible lattice, critical lattice, packing lattice, module space, packing density, optimal packing.