Editing 3D rotation group (section)

==Realizations of rotations==
{{Main|Rotation formalisms in three dimensions}}
{{see also|Charts on SO(3) }}

We have seen that there are a variety of ways to represent rotations:
* as orthogonal matrices with determinant 1,
* by axis and rotation angle
* in [[quaternion]] algebra with [[versor]]s and the map [[3-sphere]] ''S''<sup>3</sup> → SO(3) (see [[quaternions and spatial rotation]]s)
* in [[geometric algebra]] as a [[Rotor (mathematics)|rotor]]
* as a sequence of three rotations about three fixed axes; see [[Euler angle]]s.