15. Several such programs are described in the Software Review section of this issue.
16. For their classification of isohedral tilings see Griinbaum and Shephard [4
chapter 6. For Heesch's classification system see Heinrich Heesch and Otto Kienzle Fldchenschluss. System derFormen liickenlos aneinanderschliessender Flachteile (Berlin: Springer 1963). For the story of Escher's development of his own theory of tiling and classification system see Doris Schattschneider Visions of Symmetry: Notebooks Periodic Drawings and Related Work of M. C. Escher (New York: Freeman 1990). This volume includes color photos of Escher's symmetry drawings and also a reproduction of Heesch's classification chart.
17. Doris Schattschneider \"Will it Tile? Try the Conway Criterion!\" Mathematics Magazine 53 No. 4 224-233 (1980).
18. Branko Griinbaum \"Mathematical Challenges in Escher's Geometry\" in Coxeter et al. [2
pp. 53-68.
19. See Felix E. Browder ed. MathematicalDevelopments Arisingfrom the Hilbert Problems 3rd Ed. (Providence RI: American Mathematical Society 1979).
20. See Schattschneider [6
.
21. Martin Gardner \"Penrose Tiling\" and \"Penrose Tiling II\" in Penrose Tiles to Trapdoor Ciphers (New York: Freeman 1989) pp. 1-29; and Griinbaum and Shephard [4
chapter 10.
22. For detailed information on the symmetry analysis of two-color patterns see Dorothy Washburn and Donald Crowe Symmetries of Culture: Theories and Practice of Plane Pattern Analysis (Seattle WA: Univ. of Washington Press 1988). This volume contains many examples of patterns from archeological sources.
23. Escher's tilings by two tiles that contrast in form and in color (such as birds and fish) invite animation. The movie M. C. Escher: Symmetry and Space explores this. See Michele Emmer \"Movies on M. C. Escher and their Mathematical Appeal\" in Coxeter et al. [2
pp. 249-262.
24. See Schattschneider [16
.
25. See Martin Gardner 'Tiling with Polyominoes Polyiamonds and Polyhexes\" in Gardner [7
pp. 177-187.
26. See Gruinbaum and Shephard [4
section 10.1.
27. This process is demonstrated with several pairs of tiles discovered by Penrose and with a pair of triangle tiles discovered by Raphael Robinson as described in Grfinbaum and Shepard [4
section 10.3.
28. For definitions and illustrations of these tilings see Marjorie Senechal Crystalline Symmetries: An Informal Mathematical Introduction (Bristol: Adam Hilger 1990) section 3.3. For references to literature on applications see Grunbaum and Shephard [4
pp. 265-266.
29. Marjorie Senechal \"The Algebraic Escher\" Structural Topology 15 (1988) pp. 31-42.
30. William Thurston \"Conway's Tiling Groups\" American Mathematical Monthly 97 (1990) pp. 757-773.
31. See Washburn and Crowe [23
.
32. See Griinbaum and Shepard [4
chapter 11.
33. This tiling is a portion of one that appears in Stan Wagon Mathematica in Action (New York: Freeman 1991).
34. Doris Schattschneider The Fascination of Tiling.
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