The wallpaper groups are the 17 possible plane symmetry groups . They are commonly represented using Hermann-Mauguin -like
symbols or in orbifold notation (Zwillinger
1995, p. 260).
Patterns created with Artlandia SymmetryWorks for each of these groups are illustrated above.
Beautiful patterns can be created by repeating geometric and artistic motifs according to the symmetry of the wallpaper groups, as exemplified in works by M. C. Escher
and in the patterns created by I. Bakshee in the Wolfram
Language using Artlandia, illustrated above.
For a description of the symmetry elements present in each space group, see Coxeter (1969, p. 413).
See also Crystallographic Point Groups ,
Space Groups ,
Tessellation ,
Tiling
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References Artlandia. "Artlandia: Practical, Easy-to-Use Tools for Graphic Design." http://www.artlandia.com/ . Bakshee,
I. Graphica
2: The World of Mathematica Graphics. The Beauty of Random Worlds: The Art of Igor
Bakshee. Baloglou, G. "Crystallography
Now." http://www.oswego.edu/~baloglou/103/seventeen.html . Coxeter,
H. S. M. Introduction
to Geometry, 2nd ed. Escher, M. C.
"Picture Gallery 'Symmetry.' " http://www.mcescher.com/Gallery/gallery-symmetry.htm . Hilbert,
D. and Cohn-Vossen, S. Geometry
and the Imagination. Joyce, D. E.
"Wallpaper Groups (Plane Symmetry Groups)." http://aleph0.clarku.edu/~djoyce/wallpaper/ . Schattschneider,
D. "The Plane Symmetry Groups: Their Recognition and Notation." Amer.
Math. Monthly 85 , 439-450, 1978. Weyl, H. Symmetry. Zwillinger, D. (Ed.).
"Crystallographic Groups." §4.2.4 in CRC
Standard Mathematical Tables and Formulae. Referenced on Wolfram|Alpha Wallpaper Groups
Cite this as:
Weisstein, Eric W. "Wallpaper Groups."
From MathWorld https://mathworld.wolfram.com/WallpaperGroups.html
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