Gyration

This article is about rotational symmetry in mathematics. For the size measure in structural engineering, see radius of gyration. For the motion of a charged particle in an magnetic field, see gyroradius. For the tensor of second moments, see gyration tensor.

In geometry, a gyration is a rotation in a discrete subgroup of symmetries of the Euclidean plane such that the subgroup does not also contain a reflection symmetry whose axis passes through the center of rotational symmetry. In the orbifold corresponding to the subgroup, a gyration corresponds to a rotation point that does not lie on a mirror, called a gyration point.