References and Links

References

• Martin Buerger. An Introduction to the Fundamental Features of Crystals. Wiley, 1956, revised 1963.

• Philip H. Butler. Point group symmetry applications: methods and tables. Plenum Press, New York, 1981.

• H. S. M. Coxeter. Introduction to Geometry. Wiley, New York, 1961. An excellent text on modern geometry. Coxeter makes transformations and groups central concepts. See especially chapter 2 for wallpaper patterns and related topics.

• D. Hilbert and S. Cohn-Vossen. Anschauliche Geometrie. Springer, Berlin, 1932. English translation: Geometry and the Imagination. Chelsea, 1952. See especially chapter 2 of this fascinating book on geometry.

• Arthur S. Nowick. Crystal properties via group theory. Cambridge University Press, Cambridge-New York, 1995.

• Allen Nussbaum. Applied group theory for chemists, physicists and engineers. Prentice-Hall, Englewood Cliffs, N.J.,1971.

• Doris Schattschneider The plane symmetry groups: their recognition and notation, Amer. Math. Monthly 85 (1978), 439-450. This is a nice article. This journal should be available at every college library in the United States.

• Hermann Weyl.Symmetry. Princeton University Press, Princeton, 1952. Weyl wrote four relatively nonmathematical lectures on the general subject of symmetry with many examples from art and science.

Web links

• Xah has a very nice undergraduate tutorial on wallpaper groups, with illustrations of the 17 wallpaper groups and a wallpaper gallery.

• Yoshiaki Araki's pages of Escher patterns.

• Hyperbolic Tesselations of the Poincaré Disk

• Mark Newbold's POV-Ray Kaleidoscopes including some spherical tesselations

• Symmetry and the Shape of Space by Chaim Goodman Strauss

• Allan Bergmann Jensen's dynamic tesselations use the "The Geometers Sketchpad".

• Wallpaper patterns illustrating traditional Japanese patterns at the Mathematics Museum of the Tohsuke Urabe mathematics Laboratory, Japan.

• Hans Kuiper's Computer Art inspired by M.C. Escher and Victor Vasarely with many wallpaper patterns

• Symmetry in the Plane at Mathematics Education at the Memorial University of Newfoundland

• Math Tessellations at Highland Middle School

• Kurt's Look at Tilings (seems to be gone from the web ca. mid 1997)

• The Geometry Center has excerpts of the CRC Press's Standard Mathematical Tables and Formulas on line including some on Wallpaper Groups

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© 1994, 1997.

David E. Joyce
Department of Mathematics and Computer Science
Clark University
Worcester, MA 01610

The address of these files are http://aleph0.clarku.edu/~djoyce/wallpaper/