Non-fundamental trunc-simplex tilings and their optimal hyperball packings and coverings in hyperbolic space I. For families F1-F4
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. Molna ' r et al. in 2006. Our paper relies basically on this work. 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 To ' th for balls and horoballs in 1964.
Keywords:
truncated simplex / Poincar? algorithm / isometries / hyperbolic space group / fundamental domainSource:
Filomat, 2023, 37, 5, 1409-1448Publisher:
- Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš
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Institution/Community
Fakultet organizacionih naukaTY - JOUR AU - Molnar, Emil AU - Stojanović, Milica AU - Szirmai, Jeno PY - 2023 UR - https://rfos.fon.bg.ac.rs/handle/123456789/2455 AB - 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. Molna ' r et al. in 2006. Our paper relies basically on this work. 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 To ' th for balls and horoballs in 1964. PB - Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš T2 - Filomat T1 - Non-fundamental trunc-simplex tilings and their optimal hyperball packings and coverings in hyperbolic space I. For families F1-F4 EP - 1448 IS - 5 SP - 1409 VL - 37 UR - conv_2837 ER -
@article{ author = "Molnar, Emil and Stojanović, Milica and Szirmai, Jeno", year = "2023", 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. Molna ' r et al. in 2006. Our paper relies basically on this work. 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 To ' th for balls and horoballs in 1964.", publisher = "Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš", journal = "Filomat", title = "Non-fundamental trunc-simplex tilings and their optimal hyperball packings and coverings in hyperbolic space I. For families F1-F4", pages = "1448-1409", number = "5", volume = "37", url = "conv_2837" }
Molnar, E., Stojanović, M.,& Szirmai, J.. (2023). Non-fundamental trunc-simplex tilings and their optimal hyperball packings and coverings in hyperbolic space I. For families F1-F4. in Filomat Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš., 37(5), 1409-1448. conv_2837
Molnar E, Stojanović M, Szirmai J. Non-fundamental trunc-simplex tilings and their optimal hyperball packings and coverings in hyperbolic space I. For families F1-F4. in Filomat. 2023;37(5):1409-1448. conv_2837 .
Molnar, Emil, Stojanović, Milica, Szirmai, Jeno, "Non-fundamental trunc-simplex tilings and their optimal hyperball packings and coverings in hyperbolic space I. For families F1-F4" in Filomat, 37, no. 5 (2023):1409-1448, conv_2837 .