This PREP workshop was made possible by the NSF grant DUE: 0341481

From Prep08Wiki

Students always want to say a frieze pattern has cyclic C4 or dihedral D2 or some other rosette symmetry, and you often have to reiterate that frieze patterns have translations so their symmetry groups are different. Then, they do the same thing going from frieze to wallpaper. I think something like this might help them make that distinction. You could also turn the question on it's head, and once they've made the wallpaper they could look at the columns of letters and see what frieze patterns the vertical strips have. Sometimes it will match the horizontal, sometimes not.

As far as formatting, here's a couple of ways: Put a leading space:

x x x x 
x x x x
x x x x
x x x x

But that changes your font, and looks kind of ugly. You could also use a table:

x x x x

x x x x

x x x x

x x x x

More complicated, but with better control over the spacing, put each x in it's own box in the table:

x	x	x	x
x	x	x	x
x	x	x	x
x	x	x	x

As far as the wallpaper patterns go, I'll leave them as an exercise for another participant, but the way to go is to use the flowchart. It's on escherwiki:Wallpaper Patterns (among other places on the web).

Bryan 03:17, 26 June 2008 (UTC)