Horoball packings to the totally asymptotic regular simplex in the hyperbolic n-space
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چکیده
منابع مشابه
The Optimal Ball and Horoball Packings to the Coxeter Honeycombs in the Hyperbolic d-space
In a former paper [18] 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 H, (d = 4, 5), and determine the metric data of their optimal ball an...
متن کاملThe Optimal Ball and Horoball Packings of the Coxeter Tilings in the Hyperbolic 3-space
In this paper I describe a method – based on the projective interpretation of the hyperbolic geometry – that determines the data and the density of the optimal ball and horoball packings of each well-known Coxeter tiling (Coxeter honeycomb) in the hyperbolic space H.
متن کاملHoroball Packings for the Lambert - cube Tilings in the Hyperbolic 3 - space
– (p, q) (p > 2, q = 2). These infinite tiling series of cubes are the special cases of the classical Lambert-cube tilings. The dihedral angles of the Lambert-cube are πp (p > 2) at the 3 skew edges and π2 at the other edges. Their metric realization in the hyperbolic space H 3 is well known. A simple proof was described by E. Molnár in [10]. The volume of this Lambert-cube type was determined ...
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Packing problems have long been a topic of interest. Traditionally, efforts had been focused on Euclidean space, but as interest in hyperbolic space has grown, many of the Euclidean problems have been translated into the hyperbolic arena, in which the problems are almost always vastly more complicated. The particular packing problem of interest here is a hyperbolic version of packing congruent ...
متن کاملRegular Honeycombs in Hyperbolic Space
made a study of honeycombs whose cells are equal regular polytopes in spaces of positive, zero, and negative curvature. The spherical and Euclidean honeycombs had already been described by Schlaf li (1855), but the only earlier mention of the hyperbolic honeycombs was when Stringham (1880, pp. 7, 12, and errata) discarded them as "imaginary figures", or, for the two-dimensional case, when Klein...
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ژورنال
عنوان ژورنال: Aequationes mathematicae
سال: 2012
ISSN: 0001-9054,1420-8903
DOI: 10.1007/s00010-012-0158-6