Geometry | Part IB, 2002

Show that every isometry of Euclidean space R3\mathbb{R}^{3} is a composition of reflections in planes

What is the smallest integer NN such that every isometry ff of R3\mathbb{R}^{3} with f(0)=0f(0)=0 can be expressed as the composition of at most NN reflections? Give an example of an isometry that needs this number of reflections and justify your answer.

Describe (geometrically) all twelve orientation-reversing isometries of a regular tetrahedron.

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