Brief intro to the mathematical formalism used to describe rotations of the eyes in 3D (including the torsional component). The shape of the human eye is approximately a sphere with a diameter of 23 mm, and mechanically it behaves like a ball in a ball and socket joint. Because there is a functional distinguished axis - the visual axis, that is the line of gaze or more precisely the imaginary straight line passing through both the center of the pupil and the center of the fovea - the movements of the eyes are usually divided in gaze direction and cyclotorsion (or simply torsion): while gaze direction refers to the direction of the visual axis, the torsion indicates the rotation of the eyeball about the visual axis.