# Sphere Packings, Lattices and Groups

@inproceedings{Conway1988SpherePL, title={Sphere Packings, Lattices and Groups}, author={John H. Conway and N. J. A. Sloane}, booktitle={Grundlehren der mathematischen Wissenschaften}, year={1988} }

The second edition of this book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also continue to examine related problems such as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. Like the first edition, the second edition describes the applications of these questions to other areas of mathematics and science such…

## 3,235 Citations

Packing Lines, Planes, etc.: Packings in Grassmannian Spaces

- MathematicsExp. Math.
- 1996

A reformulation of the problem gives a way to describe n-dimensional subspaces of m-space as points on a sphere in dimension ½(m–l)(m+2), which provides a (usually) lowerdimensional representation than the Plucker embedding and leads to a proof that many of the new packings are optimal.

Covering of Discrete Quasiperiodic Sets: Concepts and Theory

- Mathematics
- 2002

The packing of congruent, convex, impenetrable bodies in 3-space has obvious practical applications. Mathematical analysis has extended the search for optimal packings to spaces of dimension n > 3.…

Lattices, packings and tilings in the plane

- Philosophy
- 2010

Preliminary note. For the arrangement of Chaps. IX and X, we have adopted the following policy concerning the interplay between dimension 2 and dimensions 3 and higher. In the present chapter - in…

Unit Sphere Packings

- Mathematics
- 2013

Unit sphere packings are the classical core of (discrete) geometry. We survey old as well new results giving an overview of the art of the matters. The emphases are on the following five topics: the…

Kissing numbers, sphere packings, and some unexpected proofs

- Mathematics
- 2004

The ikissing number problemi asks for the maximal number of white spheres that can touch a black sphere of the same size in n-dimensional space. The answers in dimensions one, two and three are…

Low-dimensional lattices. IV. The mass formula

- MathematicsProceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1988

The mass formula expresses the sum of the reciprocals of the group orders of the lattices in a genus in terms of the properties of any of them. We restate the formula so as to make it easier to…

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