3D rotation group
In mechanics and geometry, the 3D rotation group, often denoted SO(3), is the group of all rotations about the origin of three-dimensional Euclidean space R 3 {\displaystyle \mathbb {R} ^{3}} under the operation of composition, which combines two rotations by performing one after the other. A rotation about a point is a transformation that preserves that point, while also preserving the Euclidean distance between any two points (so it is an isometry), and orientation (i.e., handedness of space).