Congruent and non-congruent hyperball packings related to doubly truncated Coxeter orthoschemes in hyperbolic 3-space

[1] K. Bezdek, Sphere Packings Revisited, Eur. J. Combin., 27/6 (2006), 864–883.10.1016/j.ejc.2005.05.001Search in Google Scholar

[2] J. Bolyai, Appendix, Scientiam spatii absolute veram exhibens, Marosvásárhely, (1831).Search in Google Scholar

[3] K. Böröczky, Packing of spheres in spaces of constant curvature, Acta Math. Acad. Sci. Hungar., 32 (1978), 243–261.10.1007/BF01902361Search in Google Scholar

[4] K. Böröczky, A. Florian,Über die dichteste Kugelpackung im hyperbolis-chen Raum, Acta Math. Acad. Sci. Hungar., 15 (1964), 237–245.10.1007/BF01897041Search in Google Scholar

[5] G. Fejes Tóth, G. Kuperberg, W. Kuperberg, Highly Saturated Packings and Reduced Coverings, Monatsh. Math., 125/2 (1998), 127–145.10.1007/BF01332823Search in Google Scholar

[6] L. Fejes Tóth, Regular Figures, Macmillan (New York), 1964.Search in Google Scholar

[7] H. -C. Im Hof, Napier cycles and hyperbolic Coxeter groups, Bull. Soc. Math. Belgique, 42 (1990), 523–545.Search in Google Scholar

[8] R. Kellerhals, On the volume of hyperbolic polyhedra, Math. Ann., 285 (1989), 541–569.10.1007/BF01452047Search in Google Scholar

[9] R. T. Kozma, J. Szirmai, New Lower Bound for the Optimal Ball Packing Density of Hyperbolic 4-space, Discrete Comput. Geom., 53/1 (2015), 182-198, DOI: 10.1007/s00454-014-9634-1.10.1007/s00454-014-9634-1Search in Google Scholar

[10] E. Molnár, The Projective Interpretation of the eight 3-dimensional homogeneous geometries, Beitr. Algebra Geom.,38/2 (1997), 261–288.Search in Google Scholar

[11] E. Molnár, J. Szirmai, Top dense hyperbolic ball packings and coverings for complete Coxeter orthoscheme groups, Publications de l’Institut Mathématique, 103 (117) (2018), 129–146, DOI: 10.2298/PIM1817129M, arXiv: 1612.04541.10.2298/PIM1817129MSearch in Google Scholar

[12] M. Stojanović, Coxeter Groups as Automorphism Groups of Solid Transitive 3-simplex Tilings, Filomat,28/3 (2014), 557–577, DOI 10.2298/FIL1403557S.10.2298/FIL1403557SSearch in Google Scholar

[13] M. Stojanović, Hyperbolic space groups and their supergroups for fundamental simplex tilings, Acta Math. Hungar.,153/2 (2017), 276–288, DOI: 10.1007/s10474-017-0761-z.10.1007/s10474-017-0761-zSearch in Google Scholar

[14] J. Szirmai, Hyperball packings in hyperbolic 3-space, Mat. Vesn., 70/3 (2018), 211–221.Search in Google Scholar

[15] J. Szirmai, Packings with horo- and hyperballs generated by simple frustum orthoschemes, Acta Math. Hungar., 152/2 (2017), 365–382, DOI:10.1007/s10474-017-0728-0.10.1007/s10474-017-0728-0Search in Google Scholar

[16] J. Szirmai, Density upper bound of congruent and non-congruent hyper-ball packings generated by truncated regular simplex tilings, Rendiconti del Circolo Matematico di Palermo Series 2, 67 (2018), 307–322, DOI: 10.1007/s12215-017-0316-8, arXiv:1510.03208.10.1007/s12215-017-0316-8Search in Google Scholar

[17] J. Szirmai, Decomposition method related to saturated hyperball packings, Ars Math. Contemp., 16 (2019), 349–358.10.26493/1855-3974.1485.0b1Search in Google Scholar

[18] J. Szirmai, The optimal ball and horoball packings to the Coxeter honeycombs in the hyperbolic d-space, Beitr. Algebra Geom.,48/1 (2007), 35–47.Search in Google Scholar

[19] J. Szirmai, Horoball packings to the totally asymptotic regular simplex in the hyperbolic n-space, Aequat. Math., 85 (2013), 471-482, DOI: 10.1007/s00010-012-0158-6.10.1007/s00010-012-0158-6Search in Google Scholar

[20] J. Szirmai, Horoball packings and their densities by generalized simplicial density function in the hyperbolic space, Acta Math. Hungar.,136/1-2 (2012), 39–55, DOI: 10.1007/s10474-012-0205-8.10.1007/s10474-012-0205-8Search in Google Scholar

[21] J. Szirmai, The p-gonal prism tilings and their optimal hypersphere packings in the hyperbolic 3-space, Acta Math. Hungar., 111 (1-2) (2006), 65–76.10.1007/s10474-006-0034-8Search in Google Scholar

[22] J. Szirmai, The regular prism tilings and their optimal hyperball packings in the hyperbolic n-space, Publ. Math. Debrecen, 69 (1-2) (2006), 195–207.10.1007/s10474-006-0034-8Search in Google Scholar

[23] J. Szirmai, The optimal hyperball packings related to the smallest compact arithmetic 5-orbifolds, Kragujevac J. Math.40 (2) (2016), 260-270, DOI:10.5937/KgJMath1602260S.10.5937/KgJMath1602260SSearch in Google Scholar

[24] J. Szirmai, The least dense hyperball covering to the regular prism tilings in the hyperbolic n-space, Ann. Mat. Pur. Appl.195/1 (2016), 235–248, DOI: 10.1007/s10231-014-0460-0.10.1007/s10231-014-0460-0Search in Google Scholar

[25] J. Szirmai, A candidate for the densest packing with equal balls in Thurston geometries, Beitr. Algebra Geom., 55/2 (2014), 441-452, DOI: 10.1007/s13366-013-0158-2.10.1007/s13366-013-0158-2Search in Google Scholar

[26] J. Szirmai, Hyperball packings related to cube and octahedron tilings in hyperbolic space, Contributions to Discrete Mathematics, (to appear), (2020).Search in Google Scholar

[27] J. Szirmai, Upper bound of density for packing of congruent hyperballs in hyperbolic 3−space, Submitted manuscript, (2019).Search in Google Scholar

[28] I. Vermes,Über die Parkettierungsmöglichkeit des dreidimensionalen hyperbolischen Raumes durch kongruente Polyeder, Studia Sci. Math. Hungar., 7 (1972), 267–278.Search in Google Scholar

[29] I. Vermes, Ausfüllungen der hyperbolischen Ebene durch kongruente Hyperzykelbereiche, Period. Math. Hungar., 10/4 (1979), 217–229.10.1007/BF02020020Search in Google Scholar

[30] I. Vermes,Über reguläre Überdeckungen der Bolyai-Lobatschewskischen Ebene durch kongruente Hyperzykelbereiche, Period. Math. Hungar., 25/3 (1981), 249–261.Search in Google Scholar