Lets call “” A’, then the first is A A’ B’ B and the second is A’ A A’ A. If you take the first and choose B=A’, you get A A’ A A’, which is a rotated version of the second.

]]>I separately verified the same simple solution applies to both. On the other hand, it also applies to a square with four sides labeled ‘>’, ‘>>’, ‘>>>’, ‘>>>>’, so it doesn’t mean that much. (That’s an interesting conclusion, so I think you should include this general case as the last problem)

]]>In December, I worked trough your series on The Lucas-Lehmer test with one of my high school students. He and I then started studying Abstract Algebra, and I’m certain he would find wallpaper groups as interesting as I will.

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