Can Cubes Avoid Meeting Face to Face?

  • Raphael M. Robinson


In this paper, we shall study the tiling of space by congruent cubes. By saying that the cubes form a tiling of space, we mean that they cover space without overlapping. We will assume that the edges of the cubes are parallel to the coordinate axes. There is no loss of generality in using unit cubes, and we shall usually do so.


Parity Class Lattice Point Unit Cube Oblique Section Cube Face 


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  1. 1.
    Robinson, R. M. 1979. Multiple tilings of n-dimensional space by unit cubes. Mathematische Zeitschrift 166: 225–264.CrossRefGoogle Scholar
  2. 2.
    Stein, S. K. 1974. Algebraic tiling. American Mathematical Monthly 81: 445–462.CrossRefGoogle Scholar

Copyright information

© Wadsworth International 1981

Authors and Affiliations

  • Raphael M. Robinson
    • 1
  1. 1.University of CaliforniaUSA

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