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Rotational symmetry
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{{Short description|Property of objects which appear unchanged after a partial rotation}} {{Use American English|date = March 2019}} {{more citations needed|date=June 2018}} [[File:The armoured triskelion on the flag of the Isle of Man.svg|thumb|The [[triskelion]] appearing on the [[Flag of the Isle of Man|Isle of Man flag]] has rotational symmetry because it appears the same when rotated by one third of a full turn about its center. Because its appearance is identical in three distinct orientations, its rotational symmetry is three-fold.]] '''Rotational symmetry''', also known as '''radial symmetry''' in [[geometry]], is the property a [[shape (geometry)|shape]] has when it looks the same after some [[rotation (mathematics)|rotation]] by a partial [[turn (angle)|turn]]. An object's degree of rotational symmetry is the number of distinct [[Orientation (geometry)|orientations]] in which it looks exactly the same for each rotation. Certain geometric objects are partially symmetrical when rotated at certain angles such as [[squares]] rotated 90°, however the only geometric objects that are fully rotationally symmetric at any angle are spheres, circles and other [[spheroids]].<ref>[https://arxiv.org/pdf/1807.09654.pdf Rotational symmetry of Weingarten spheres in homogeneous three-manifolds. By Jos ́e A. G ́alvez, Pablo Mira]</ref><ref>[https://www.researchgate.net/profile/Dmitrii-Maksimov/publication/317939298_Topological_Bound_States_in_the_Continuum_in_Arrays_of_Dielectric_Spheres/links/5a58a612aca2725b780773f5/Topological-Bound-States-in-the-Continuum-in-Arrays-of-Dielectric-Spheres.pdf Topological Bound States in the Continuum in Arrays of Dielectric Spheres. By Dmitrii N. Maksimov, LV Kirensky Institute of Physics, Krasnoyarsk, Russia]</ref>
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