The Mathematical Intelligencer

, Volume 17, Issue 2, pp 41–51 | Cite as

Tilings of space by knotted tiles

  • Colin C. Adams


Boundary Component Solid Torus Heegaard Splitting Threefold Symmetry Tile Space 
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  1. 1.
    C. Adams,The Knot Book, New York: W. H. Freeman and Co., 1994.MATHGoogle Scholar
  2. 2.
    T. Banchoff, Torus decompositions of regular polytopes in 4-space, inShaping Space—A Polyhedral Approach, edited by M. Senechal and G. Fleck, Boston: Birkhäuser, 1988.Google Scholar
  3. 3.
    H. S. M. Coxeter and G. C. Shephard, Regular 3-complexes with toroidal cells,J. Comb. Theory B 22 (1977), 131–138.CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    H. E. Debrunner, Tiling three-space with handlebodies,Studia Scientiarum Mathematicarum Hungarica 21 (1986), 201–202.MATHMathSciNetGoogle Scholar
  5. 5.
    V. Frei, O osmnactem Hilbertove problemy,Pokroky Matematiky, Fysiky Astronomie 20 (1975), 260–268 (in Czech).MATHMathSciNetGoogle Scholar
  6. 6.
    B. Grunbaum and G. C. Shephard,Tilings and Patterns, New York, W. H. Freeman and Co., 1987.Google Scholar
  7. 7.
    W. Kuperberg, Knotted lattice-like space fillers,Discrete Comput. Geom. (in press).Google Scholar
  8. 8.
    E. E. Moise, Affine structures in 3-manifolds V. The Triangulation theorem and Hauptvermutung,Ann. Math. 56 (1952), 96–114.CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    K. Reinhardt, Zur Zerlegung der euklidischen Raume in kongruente Polytope,S.-Ber. Preuss. Akad. Wiss. Berlin (1928), 150–155.Google Scholar
  10. 10.
    D. Rolfsen,Knots and Links, Publish or Perish Press, Berkeley 1976.Google Scholar
  11. 11.
    P. Schmitt, A spacefilling cloverleaf knot, preprint.Google Scholar
  12. 12.
    E. Schulte, Space fillers of higher genus,J. Comb. Theory A 68, no. 2 (1994), 438–453.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 1995

Authors and Affiliations

  • Colin C. Adams
    • 1
  1. 1.Department of MathematicsWilliams CollegeWilliamstownUSA

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