Paper 3, Section II, D

Groups | Part IA, 2009

State and prove the orbit-stabilizer theorem.

Let GG be the group of all symmetries of a regular octahedron, including both orientation-preserving and orientation-reversing symmetries. How many symmetries are there in the group GG ? Let DD be the set of straight lines that join a vertex of the octahedron to the opposite vertex. How many lines are there in the set DD ? Identify the stabilizer in GG of one of the lines in DD.

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