MMN-2959

Geodesic ball packings generated by regular prism tilings in Nil geometry

  • Benedek Schultz, Budapest University of Technology and, Economics Institute of Mathematics, Department of Geometry, schultzb@math.bme.hu
  • JenÅ‘ Szirmai, Budapest University of Technology and, Economics Institute of Mathematics, Department of Geometry, szirmai@math.bme.hu

Abstract

In this paper we study the regular prism tilings and construct ball packings by geodesic balls related to the above tilings in the projective model of Nil geometry. Packings are generated by action of the discrete prism groups pq21. We prove that these groups are realized by prism tilings in Nil space if (p, q) = (3, 6), (4, 4) or (6, 3) and determine packing density formulae for geodesic ball packings generated by the above prism groups. Moreover, studying these formulae we determine the conjectured maximal dense packing arrangements and their densities and visualize them in the projective model of Nil geometry. We get a dense (conjectured locally densest) geodesic ball arrangement related to the parameters (p, q) = (6, 3) where the kissing number of the packing is 14, similarly to the densest lattice-like Nil geodesic ball arrangement investigated by the second author.


Vol. 23 (2022), No. 1, pp. 429-442
DOI: 10.18514/MMN.2022.2959


Download: MMN-2959