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Escher-Like Patterns from Pentagonal Tilings

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M.C. Escher’s Legacy


My first acquaintance with tiling pentagons was from Martin Gardner’s “Mathematical Games” columns in Scientific American magazine, in July and in December 1975. Although every triangle and every quadrilateral can tile the plane (that is, fill the plane with congruent copies, without gaps or overlaps), only certain types of pentagons can tile the plane. Until Gardner’s article, it was believed that all such types were known; there were eight different types.

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  1. Martin Gardner July 1975. “On tessellating the plane with convex polygon tiles.” Mathematical Games, Scientific American, pp. 112–117.

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  2. Martin Gardner 1988. “Tiling with Convex Polygons.” Time Travel and other Mathematical Bewilderments. W.H. Freeman & Co. pp. 174–175. [This reproduces the 1975 column of [1] and gives updates on the aftermath of the column.]

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  3. Daniel Huson and Olaf Delgado Friedrichs 1992–95. RepTiles, computer software to produce k-isohedral tilings.

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  4. Ivars Peterson 1990. “Paving the Plane.” Islands of Truth. W.H. Freeman & Co. pp. 83–86.

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  5. Doris Schattschneider 1981. “In Praise of Amateurs.” The Mathematical Gardner, edited by David A. Klarner. Wadsworth International, pp. 140–166.

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  6. Doris Schattschneider. Jan. 1978. “Tiling the Plane with Congruent Pentagons.” Mathematics Magazine, pp. 29–44.

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  7. Doris Schattschneider Nov. 1985. “A New Pentagon Tiler.” Mathematics Magazine, cover and News and Notes.

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  8. Doris Schattschneider and Marjorie Rice. Dec. 1980. “The Incredible Pentagonal Versatile.” Mathematics Teaching pp. 52–53.

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  9. Doris Schattschneider 1990. Visions of Symmetry: Notebooks, Periodic Drawings, and Related Work of M.C. Escher. New York: W.H. Freeman & Co.

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Rice, M. (2003). Escher-Like Patterns from Pentagonal Tilings. In: Schattschneider, D., Emmer, M. (eds) M.C. Escher’s Legacy. Springer, Berlin, Heidelberg.

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