Gyration

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.^[1]

For example, having a sphere rotating about any point that is not the center of the sphere, the sphere is gyrating. If it was rotating about its center, the rotation would be symmetrical and it would not be considered gyration.

References

^ Liebeck, Martin W.; Saxl, Jan; Hitchin, N. J.; Ivanov, A. A. (1992-09-10) [1990]. Groups, Combinatorics & Geometry. Lecture note series. Vol. 165 (illustrated ed.). Symposium, London Mathematical Society: Symposium on Groups and Combinatorics (1990), Durham: Cambridge University Press. ISBN 0-52140685-4. ISSN 0076-0552. ISBN 978-0-52140685-7. Retrieved 2010-04-07.{{cite book}}: CS1 maint: location (link) (489 pages)

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[Liebeck-1] Liebeck, Martin W.; Saxl, Jan; Hitchin, N. J.; Ivanov, A. A. (1992-09-10) [1990]. Groups, Combinatorics & Geometry. Lecture note series. Vol. 165 (illustrated ed.). Symposium, London Mathematical Society: Symposium on Groups and Combinatorics (1990), Durham: Cambridge University Press. ISBN 0-52140685-4. ISSN 0076-0552. ISBN 978-0-52140685-7. Retrieved 2010-04-07.{{cite book}}: CS1 maint: location (link) (489 pages)

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