Dear Dr. Mills,

The 17 wallpaper groups demonstrated using periodic tilings drawn by RepTiles. The tilings are all four-colorable, i.e. each has four equivalence classes of tiles, s.t. no two tiles of the same class share an edge. Moreover, the tilings have maximal symmetry, meaning that they is no topologically equivalent tiling with higher symmetry.

If you find these tilings too complex, then I could easily produce ones with less classes of tiles, but they look rather boring. Alternately, you can easily produce such pictures yourself using the RepTiles program. To convert RepTiles pictures in to postscript, simply choose the laserprinter with the macintosh chooser and then print the tilings to postscipt files by pressing the appropriate button in the printer dialog.

Best wishes Daniel Huson

Below are listed examples of the seventeen plane symmetry groups, generated by Daniel Huson using his RepTile program.

p1 gif_icon pm gif_icon pmmgif_icon pg gif_icon pgggif_icon pmggif_icon p2 gif_icon p3 gif_icon p31mgif_icon p3m1gif_icon p4 gif_icon p4ggif_icon p4mgif_icon p6 gif_icon p6mgif_icon cm gif_icon cmmgif_icon

am 3/5/95