Math 236H Spring, 2008.
Wallpaper groups and related topics

• Xah Lee's wallpaper groups page (220 KB file with lots of graphics) Includes a very helpful table showing the patterns and symmetries associated with each group and extensive annotated reference section. This page is part of a larger site about groups acting on the plane. Warning: Lee's numbering of the groups differs from that of Joyce and Science U (the next two listed below) in that 14 and 15 are interchanged.
  
  
• David Joyce's Wallpaper Groups page Colorful site with a separate page for each group that carefully explains its symmetries. It has informative history and reference pages.
  
  
• Science U's page with animations Part of a larger site about tilings and tesselations. Includes a link to Kali, an interactive program for creating symmteric designs; it takes a long time to download.
  
  
• Hop's "17 wallpaper groups" page. Has links to similar pages about Escher and Arabic tiles.
  
  
• Japanese Wallpaper Part of a larger "Mathematical Museum" site created in Japan. Includes an examination page that tests your skills at recognizing symmetry. The Japanese have names for each of the 17 wallpaper patterns!
  
  
• Dror Bar-Natan's tilings page. This page has some interesting links that are worth exploring. Dror Bar-Natan is an Israeli topologist now living in Toronto. Ask me (or read his website) about his involvement in debunking the Bible code.
  
  
• Frieze Patterns in Cast Iron Frieze groups are the 1-dimensional analog of wallpaper groups. This site explains the 7 (rather than 17) frieze groups and shows many architectural examples of them.
  
  
• The Alhambra is a mosque in Grenada, Spain famous for its beautiful mosaics. They may or may not contain patterns for each of the 17 wallpaper groups. What Symmetry Groups Are Present in the Alhambra? is a scholarly paper (2006) on this subject by Branko Grünbaum, an expert on the subject of tilings. A related paper is THE FOUR REGULAR MOSAICS MISSING IN THE ALHAMBRA (1986) by R. Perez-Gomez.
  
  
• Geometry Center wallpaper groups page Part of extensive site devoted to geometry.
  
  
• Mathworld's wallpaper groups page Also part of a much larger site about mathematics, publisheded by Wolfram Research, the creator of Mathematica.
  
  
• Wikipedia's wallpaper groups page (23 pages) Extensive, lavishly illustrated article, part of an all-purpose online encyclopedia. It includes an explanation of why there are 17 (no less and no more) wallpaper groups. A picture from this site appears as one of the "random math images" on the department home page. You can see different random images there by reloading the page.
  
  
• Java Kali link. An applet that allows experimentation with pattern creation, Java Kali can create any of the ornamental patterns (frieze, rosette, wallpaper).
  
  
• The Seventeen Wallpaper Groups Michael E. McCallum's description of the groups using the notation of John Conway, inventor of the Game of Life and the Look-and-say sequence.
  
  
• Identifying the 17 Plane Symmetry Groups Quick reference table for the 17 groups, illustrating each with a pattern that it acts on.
  
  
• 17 WALLPAPER GROUPS poster Illustrates each group with a pattern of flying animals.