The kissing number in four dimensions

By O. Musin. 2003

192 citations recorded by the source corpus.

The kissing number problem asks for the maximal number k(n) of equal size nonoverlapping spheres in n-dimensional space that can touch another sphere of the same size. This problem in dimension three was the subject of a famous discussion between Isaac Newton and David Gregory in 1694. In three dimensions the problem was finally solved only in 1953 by Schutte and van der Waerden. In this paper we present a solution of a long-standing problem about the kissing number in four dimensions. Namely, the equality fc(4) = 24 is proved. The proof is based on a modification of Delsarte's method.

Subfields: Computer Graphics and Computer-Aided Design, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/8c2509ad034b085d4cd96e6cd8751aefce7a9f39

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Graphics and Computer-Aided Design

1. Magnus Karlsson
2. Erik Agrell
3. Frank H. Stillinger
4. Salvatore Torquato

In Geometry and Topology

1. Magnus Karlsson
2. Erik Agrell
3. Frank H. Stillinger
4. Salvatore Torquato

In Numerical Analysis

1. Magnus Karlsson
2. Erik Agrell
3. Frank H. Stillinger
4. Salvatore Torquato

Citations in the corpus

• Power-Efficient Modulation Formats in Coherent Transmission Systems (2009, background): “Like many sphere packing problems, rigorous proof are difficult, and although was long conjectured [33], it was only recently proven formally [34].”
• Jammed hard-particle packings: From Kepler to Bernal and beyond (2010, background): “The optimal kissing number τmax in dimensions greater than three is only known for R 4 (Musin, 2008), R(8) and R(24) (Levenshtein, 1979; Odlyzko and Sloane, 1979).”