The Optimal Ball and Horoball Packings of the Coxeter Tilings in the Hyperbolic 3-space
نویسندگان
چکیده
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.
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 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 ...
متن کاملThe Symmetry of Optimally Dense Packings
This is a slightly expanded version of a talk given at the János Bolyai Conference on Hyperbolic Geometry, held in Budapest in July, 2002. The general subject of the talk was the densest packings of simple bodies, for instance spheres or polyhedra, in Euclidean or hyperbolic spaces, and describes recent joint work with Lewis Bowen. One of the main points was to report on our solution of the old...
متن کاملLorentzian Coxeter Groups and Boyd-Maxwell Ball Packings
In the recent study of infinite root systems, fractal patterns of ball packings were observed while visualizing roots in affine space. In fact, the observed fractals are exactly the ball packings described by Boyd and Maxwell. This correspondence is a corollary of a more fundamental result: given a geometric representation of a Coxeter group in Lorentz space, the set of limit directions of weig...
متن کاملMetric and periodic lines in the Poincare ball model of hyperbolic geometry
In this paper, we prove that every metric line in the Poincare ball model of hyperbolic geometry is exactly a classical line of itself. We also proved nonexistence of periodic lines in the Poincare ball model of hyperbolic geometry.
متن کامل