Chapter 9.1 Sphere packings and packings of ellipsoids

Mathematical, physical and chemical tables

First Online Edition (2006)

Part 9. Basic structural features

  1. E. Koch,
  2. W. Fischer

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000617

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Koch, E. and Fischer, W. 2006. Sphere packings and packings of ellipsoids. International Tables for Crystallography. C:9:9.1:746–751.

Author Information

  1. Institut für Mineralogie, Petrologie und Kristallographie, Universität Marburg, Hans‐Meerwein‐Strasse, D‐35032 Marburg, Germany

Publication History

  1. Published Online: 1 JAN 2006



Homogeneous and heterogeneous sphere packings and packings of circles together with their densities are defined, and a classification into types of sphere packings and types of circle packings is introduced. Some properties of the 11 types of homogeneous circle packings are described in a table. As the derivation of all types of homogeneous sphere packings is not yet complete, a corresponding table presents only examples with high coordination numbers (10 to 12) and respective high densities and with low coordination numbers (3 and 4) and extremely low densities. The application of sphere packings to the description of inorganic crystal structures is demonstrated by examples. Interpenetrating sphere packings and their relations to other crystallographic problems are discussed. A short survey on the problem of packings of ellipses or ellipsoids is given.


  • basic structural features;
  • ellipse and ellipsoid packing;
  • interpenetrating packing;
  • packing