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Coxeter- Exercise 5.3.1

Exercise 5.3.1 Given six collinear points A, B, C, D, E, F, consider the three involutions (AB)(DE), (BC)(EF), (CD)(FA). If any two of these involutions have a common pair, all three have a common pair. Drag any one point O, O1, or O2 onto another one of those points or stack all three, at least two of the involutions will have a common pair forcing the third to be in common with the other two as well.