Regular Structures

  • Arthur L. Loeb
Part of the Design Science Collection book series (DSC)


In Chapter 5 we discussed statistical symmetry, the fact that the average values of the valencies of structures obey some very rigid restrictions. The present chapter is the very antithesis of Chapter 5, for here we examine structures in which all elements of any one dimensionality have identical sets of valencies. Here the average values become the values of the valencies.


Space Structure Regular Structure Internal Cell Soap Film Central Edge 
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  1. 1.
    Cf., for instance, Arthur L. Loeb: Color and Symmetry (Wiley, New York, 1971), p. 33, theorem 10.Google Scholar
  2. 2.
    H. S. M. Coxeter: Introduction to Geometry (Wüey, New York, 1961), Section 22.3.MATHGoogle Scholar

Copyright information

© Arthur L. Loeb 1991

Authors and Affiliations

  • Arthur L. Loeb
    • 1
  1. 1.Department of Visual and Environmental Studies, Carpenter Center for the Visual ArtsHarvard UniversityCambridgeUSA

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