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

Contact Numbers for Congruent Sphere Packings in Euclidean 3-Space

The contact graph of an arbitrary finite packing of unit balls in Euclidean 3-space is the (simple) graph whose vertices correspond to the packing elements and whose two vertices are connected by an edge if the corresponding two packing elements touch each other. One of the most basic questions on contact graphs is to find the maximum number of edges that a contact graph of a packing of n unit ...

Average Kissing Numbers for Non-congruent Sphere Packings

The 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.

1 3 M ay 1 99 4 Average kissing numbers for non - congruent sphere packings

(The appearance of the number of the beast in the lower bound is purely coincidental.) The supremal average kissing number k is defined in any dimension, as are kc, the supremal average kissing number for congruent ball packing, and ks, the maximal kissing number for a single ball surrounded by congruent balls with disjoint interiors. (Clearly, kc ≤ k and kc ≤ ks.) It is interesting that k is a...

Dense packings of congruent circles in a circle

The problem of finding packings of congruent circles in a circle, or, equivalently, of spreading points in a circle, is considered. Two packing algorithms are discussed, and the best packings found of up to 65 circles are presented.