Paper 1, Section I, F

Geometry of Group Actions
Part II, 2010

Explain what it means to say that GG is a crystallographic group of isometries of the Euclidean plane and that Gˉ\bar{G} is its point group. Prove the crystallographic restriction: a rotation in such a point group Gˉ\bar{G} must have order 1,2,3,41,2,3,4 or 6 .