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arXiv · 2003.13631

Non-fundamental trunc-simplex tilings and their optimal hyperball packings and coverings in hyperbolic space I. For families F1-F4

Emil Molnár·Milica Stojanović·Jenő Szirmai
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Abstract

Supergroups of some hyperbolic space groups are classified as a continuation of our former works. Fundamental domains will be integer parts of truncated tetrahedra belonging to families F1 - F4, for a while, by the notation of E. Moln\'{a}r et al. in $2006$. As an application, optimal congruent hyperball packings and coverings to the truncation base planes with their very good densities are computed. This covering density is better than the conjecture of L.~Fejes~T\'oth for balls and horoballs in $1964$.

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Emil Molnár, Milica Stojanović, Jenő Szirmai. 2020-03-30. Non-fundamental trunc-simplex tilings and their optimal hyperball packings and coverings in hyperbolic space I. For families F1-F4. https://arxiv.org/abs/2003.13631

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