Space-filling Polyhedra

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


In the previous chapter we defined a space filler as a cell whose replicas together can fill all of space without having any voids between them. We saw that all Dirichlet Domains are space fillers, but that not all space fillers are necessarily Dirichlet Domains.


Space Structure Coordination Polyhedron Space Filler Lattice Complex Short Vector 
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    Cf. Cyril S. Smith: in Hierarchical Structures, L. L. Whyte, A. G. Wilson, and D. Wilson, eds. (American Elsevier, New York, 1969).Google Scholar
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    Cf. W. Fischer, H. Burzlaff, E. Hellner, and J. D. H. Donnay: Space Groups and Lattice Complexes (U.S. Department of Commerce, 1973).Google Scholar
  3. 3.
    Cf. “Coupler,” in R. Buckminster Fuller, E. J. Applewhite and A. L. Loeb: Synergetics (Macmillan, New York, 1975), pp. 541–549.Google Scholar
  4. 4.
    A. L. Loeb: J. Solid State Chem. 1, 237–267 (1970).CrossRefGoogle 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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