Isometries of the Plane, Euclidean space $R^3$ and isometries of the Platonic polyhedra.

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I want to study the isometries of plane, Euclidean space, and the platonic polyhedra. I am new to this topics. Can any one suggest books that contain these topic with details and basic explanation through algebraic approach.

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I'd suggest "Regular Polytopes" from H.S.M. Coxeter.
It even deals with $\mathbb{R}^4$ and beyond.

--- rk