Who is asking: Student
I am doing a research project on frieze patterns (also called band patterns or border patterns). I know that there are exactly seven different types of frieze patterns, but I have been unable to find a proof for this. If you could tell me this proof, or tell me some internet sites on which I can find material on this, I would be very grateful.
Proof outlines can be found in lots of recent books dealing with
geometry. For example, Coxeter, INTRODUCTION TO GEOMETRY (1969) section
3.7 (pp. 47-49).
But you can prove it yourself faster than looking up the proof.
There are only 5 types of isometries that map a horizontal strip to itself:
I hope this helps.
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