1.I.1B

Algebra and Geometry | Part IA, 2002

(a) State the Orbit-Stabilizer Theorem for a finite group GG acting on a set XX.

(b) Suppose that GG is the group of rotational symmetries of a cube CC. Two regular tetrahedra TT and TT^{\prime} are inscribed in CC, each using half the vertices of CC. What is the order of the stabilizer in GG of TT ?

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