Introductory References about Tessellations (tilings) and Sources for Illustrations

My recommendation for the best introduction to making tessellations is the book Introduction to Tessellations by Britton and Seymour. The comprehensive collection of Escher's drawings of tessellations is in Visions of Symmetry by Schattschneider.

There are many articles on tessellations in The Mathematics Teacher and Mathematics Teaching (the journal of the British Association of Mathematics Teachers). Only a few of these articles are listed below.

Dover Books has a very rich offering of books that have examples of tessellations. Two recently published books on polyominoes (one by George Martin, published by the MAA, the other by Solomon Golomb, published by Princeton University Press) contain tiling recreations; see also books by Martin Gardner that contain reprints and updates of his previous Scientific American columns, several of which discussed tilings.

• Bøggild, J.K., "Breeding Tessellations." Mathematics Teaching 90 (1980): 31-36.
• Boles, Martha and Newman, Rochelle, The Surface Plane, The Golden Relationship: Art, Math & Nature, Book 2.
  Bradford, MA: Pythagorean Press, 1992.
• Boswell, Thom, ed., The Kaleidoscope Book: A Spectrum of Spectacular Scopes to Make.
  New York: Sterling Publishing, 1992.
• Bourgoin, J., Arabic Geometrical Pattern and Design.
  New York: Dover, 1973. (Plates of original, 1879.)
• Britton, Jill, and Dale Seymour, Introduction to Tessellations.
  Palo Alto: Dale Seymour Publications, 1989.
• Critchlow, Keith, Islamic Patterns. An Analytical and Cosmological Approach.
  New York: Schocken Books, 1976.
• Crowe, Donald W., Symmetry, Rigid Motions, and Patterns, HIMAP module 4.
  Arlington MA: COMAP, 1987.
• Edwards, Lois and Kevin Lee, TesselMania! Math Connection.
  Berkeley: Key Curriculum Press, 1994.
• El-Said, Issam and Ayse Parman, Geometric Concepts in Islamic Art.
  London: World of Islam Festival Publishing Company, 1976. (Available from Dale Seymour Publications.)
• Field, Robert, Geometric Patterns from Roman Mosaics and how to draw them.
  Stradbroke (England): Tarquin Publications, 1988.
• Gardner, Martin, "Tiling with Polyominoes, Polyiamonds, and Polyhexes." Time Travel and Other Mathematical Bewilderments.
  New York: W.H. Freeman, 1988.
• Dr. Matrix's informational WWW page on Penrose tilings: http://www.infi.net/~drmatrix/progchal.htm
• Giftwrap by Artists: M.C. Escher.
  New York, Harry Abrams, 1987. (Look for others, too.)
• Grünbaum, Branko and Geoffrey Shephard, Tilings and Patterns.
  New York: W. H. Freeman, 1987.
• Haak, S. "Transformation Geometry and the Artwork of M. C. Escher." Mathematics Teacher 69 (1976): 647-652.
• Hargittai, I. and M. Hargittai, Symmetry, A Unifying Concept.
  Bolinas, CA: Shelter Publications, 1994. Also available from Key Curriculum Press.
• Hoffer, Alan and George Bratton, Kaleidoscope Math.
  Palo Alto, CA: Creative Publications, 1978.
• Hofstadter, Douglas, "Parquet Deformations: Patterns of Tiles that Shift Gradually in One Dimension." Scientific American (July 1983) 14-20.
• Jones, Owen, The Grammar of Ornament.
  New York: Van Nostrand Reinhold, 1972. (Original 1856) Plates only, New York: Dover, 1988.
• Kappraff, Jay, Connections: The Geometric Bridge Between Art and Science.
  New York: McGraw-Hill, 1991.
• Lockwood, E.H. and R.H. Macmillan, Geometric Symmetry.
  Cambridge: Cambridge University Press, 1978.
• The Mathematics Teacher 67, no. 4 (1974). (Special issue on tessellations.)
• O'Daffer, Phares and Stanley Clemens, Geometry: An Investigative Approach.
  Menlo Park, CA: Addison Wesley, 1976; second edition 1992.
• Pearce, Peter, Structure in Nature is a Strategy for Design.
  Cambridge, MA: M. I. T. Press, 1978.
• Racinet, Auguste, L'ornement polychrome.
  Paris: Firmin-Didot, 1869-1873. Plates only, Racinet's Historic Ornament in Full Color (ser. 1) and Full-Color Picture Sourcebook of Historic Ornament. New York: Dover, 1988, 1989.
• Ranucci, E. R., and J. L. Teeters, Creating Escher-Type Drawings.
  Palo Alto, CA: Creative Publications, 1977.
• Rigby, J. F., "Napolean, Escher, and Tessellations." Mathematics Magazine 64 (1991): 242-246.
• Schattschneider, Doris, "In Black and White: How to Create Perfectly Colored Symmetric Patterns." Symmetry: Unifying Human Understanding, ed. I. Hargittai, pp. 673-695.
  New York: Pergamon, 1986.
• Schattschneider, Doris, "The Fascination of Tiling." Leonardo 25, no 3/4 (1992): 341-348.
  Reprinted in The Visual Mind: Art and Mathematics, ed. Michele Emmer, pp. 157-164. Boston: MIT Press, 1994.
• Schattschneider, Doris, "In Praise of Amateurs." The Mathematical Gardner, ed. David A. Klarner, pp. 140-166. Boston: Prindle, Weber & Schmidt (now Wadsworth).
• Schattschneider, Doris, "The Plane Symmetry Groups, Their Recognition and Notation." American Mathematical Monthly 85 (1978): 439-450.
• Schattschneider, Doris, "Tiling the Plane with Congruent Pentagons," Mathematics Magazine 51 (1978) : 29-44.
• Schattschneider, Doris, "Will it Tile? Try the Conway Criterion!" Mathematics Magazine 53 (1980): 224-233.
• Schattschneider, Doris, Visions of Symmetry: Notebooks, Periodic Drawings and Related Work of M. C. Escher.
  New York: W.H. Freeman, 1990.
• Schattschneider, Doris and Wallace Walker, M.C. Escher Kaleidocycles.
  Petaluma, CA: Pomegranate Publications, 1987.
• Senechal, Marjorie, "Escher Designs on Surfaces." M. C. Escher: Art and Science, ed. Coxeter, H.S. M., M. Emmer, R. Penrose, and M. L. Teuber.
  Amsterdam: North Holland, 1986.
• Senechal, Marjorie, Quasicrystals and Geometry.
  Cambridge University Press, 1995.
• Serra, Michael, Discovering Geometry, An Inductive Approach.
  Berkeley: Key Curriculum Press, 1993.
• Stevens, Peter S., Handbook of Regular Patterns: An Introduction to Symmetry in Two Dimensions.
  Cambridge, MA: MIT Press, 1980.
• Wade, David, Pattern in Islamic Art.
  Woodstock, NY: Overlook, 1976.
• Washburn, Dorothy K. and Donald W. Crowe, Symmetries of Culture: Theory and Practice of Plane Pattern Analysis.
  Seattle, WA: University of Washington Press, 1988.
• Wiltshire, Alan, Symmetry Patterns: The art of making beautiful patterns from special grids. Stradbroke (England): Tarquin Publications, 1989.
• Yaglom, I. M., Geometric Transformations I. Washington DC: Mathematical Association of America, New Mathematical Library no. 8.

Films and videotapes

Isometries (S. Schuster, W.O.J. Moser), College Geometry Project, 1967. Available from International Film Bureau, Chicago. (16 mm color & VHS videotape, 26 min.)

Sets of tiles and tiling games

There are several commercially available sets of tiles and tiling games. Actually building a tiling with cut-out tiles is one of the best ways to come to understand its properties. Check the catalogs of distributors of mathematics supplemental teaching materials such as Dale Seymour, Creative Publications, Cuisenaire, and Tarquin (British). Also check the shops and catalogs of art museums and science museums.

Pattern Blocks and other activity tiles can be used to explore tessellations with simple polygon tiles. Pentaplex produces variations on the aperiodic sets of Penrose tiles; Kadon Enterprises has several tiling puzzles; Tessera (Damert Company) has 8 different bugs that fit together in many different ways.

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Created: Sep 18 1996 --- Last modified: Thu Dec 5 15:57:58 1996