High Quality Content by WIKIPEDIA articles! In mechanics and geometry, the rotation group is the group of all rotations about the origin of three-dimensional Euclidean space R3 under the operation of composition. By definition, a rotation about the origin is a linear transformation that preserves length of vectors (it is an isometry) and preserves orientation (i.e. handedness) of space. A length-preserving transformation which reverses orientation is called an improper rotation. Every improper rotation of three-dimensional Euclidean space is a reflection in a plane through the origin.

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