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Aperiodic tilings in higher dimensions


Author: Charles Radin
Journal: Proc. Amer. Math. Soc. 123 (1995), 3543-3548
MSC: Primary 52C22
DOI: https://doi.org/10.1090/S0002-9939-1995-1277129-X
MathSciNet review: 1277129
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Abstract: We show that in dimensions $ d \geq 3$, aperiodic tilings can naturally avoid more symmetries than just translations.


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  • [1] D. Berend and C. Radin, Are there chaotic tilings?, Comm. Math. Phys. 152 (1993), 215-219. MR 1210166 (94g:58117)
  • [2] R. Berger, The undecidability of the domino problem, Mem. Amer. Math. Soc., vol. 66, Amer. Math. Soc., Providence, RI, 1966. MR 0216954 (36:49)
  • [3] N. G. de Bruijn, Algebraic theory of Penrose's non-periodic tilings of the plane, Kon. Nederl. Akad. Wetensch. Proc. Ser. A 84 (1981), 39-66.
  • [4] L. Danzer, A single prototile, which tiles space, but neither periodically nor quasiperiodically, University of Dortmund, 1993, preprint.
  • [5] M. Gardner, Extraordinary nonperiodic tiling that enriches the theory of tiles, Sci. Amer. (1977), 116-119.
  • [6] B. Grünbaum and G. C. Shephard, Tilings and patterns, Freeman, New York, 1986.
  • [7] D. Myers, Nonrecursive tilings of the plane, II, J. Symbolic Logic 39 (1974), 286-294. MR 0363856 (51:111)
  • [8] M. Queffélec, Substitution dynamical systems-spectral analysis, Lecture Notes in Math., vol. 1294, Springer-Verlag, Berlin and New York, 1987. MR 924156 (89g:54094)
  • [9] C. Radin, Disordered ground states of classical lattice models, Rev. Math. Phys. 3 (1991), 125-135. MR 1121466 (92g:82007)
  • [10] -, Global order from local sources, Bull. Amer. Math. Soc. (N.S.) 25 (1991), 335-364. MR 1094191 (92e:82007)
  • [11] -, The pinwheel tilings of the plane, Ann. of Math. (2) 139 (1994), 661-702. MR 1283873 (95d:52021)
  • [12] -, Space tilings and substitutions, Geom. Dedicata (to appear). MR 1334449 (96b:52033)
  • [13] -, Symmetry of tilings of the plane, Bull. Amer. Math. Soc. (N.S.) 29 (1993), 213-217. MR 1215313 (94g:28022)
  • [14] C. Radin and M. Wolff, Space tilings and local isomorphism, Geom. Dedicata 42 (1992), 355-360. MR 1164542 (93c:52019)
  • [15] P. Schmitt, An aperiodic prototile in space, University of Vienna, 1988, preprint.
  • [16] H. Wang, Proving theorems by pattern recognition II, Bell Systs. Tech. J. 40 (1961), 1-41.
  • [17] -, Notes on a class of tiling problems, Fund. Math. 82 (1975), 295-305. MR 0363854 (51:109)

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DOI: https://doi.org/10.1090/S0002-9939-1995-1277129-X
Article copyright: © Copyright 1995 American Mathematical Society

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