Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 48, No. 1, pp. 35-47 (2007)

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The optimal ball and horoball packings to the Coxeter honeycombs in the hyperbolic \boldmath$d$-space

Jen\H o Szirmai

Budapest University of Technology and Economics, Institute of Mathematics, Department of Geometry, H-1521 Budapest, Hungary, e-mail:

Abstract: In a former paper [Sz] a method is described that determines the data and the density of the optimal ball or horoball packing to each Coxeter tiling in the hyperbolic $3$-space. In this work we extend this procedure--based on the projective interpretation of the hyperbolic geometry--to higher dimensional Coxeter honeycombs in $\mathbb{H}^d, \ (d=4,5)$, and determine the metric data of their optimal ball and horoball packings, respectively. [Sz] Szirmai, J.: The optimal ball and horoball packings of the Coxeter tilings in the hyperbolic $3$-space. Beitr. Algebra Geom. {\bf 46}(2) (2005), 545--558.

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Electronic version published on: 14 May 2007. This page was last modified: 27 Jan 2010.

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