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Rotational symmetry
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===Rotational symmetry with respect to any angle===<!-- [[axisymmetric]], [[axisymmetrical]] and [[axisymmetry]] redirect to here --> Rotational symmetry with respect to any angle is, in two dimensions, [[circular symmetry]]. The fundamental domain is a [[Line (mathematics)#Ray|half-line]]. In three dimensions we can distinguish ''[[cylindrical symmetry]]'' and ''[[spherical symmetry]]'' (no change when rotating about one axis, or for any rotation). That is, no dependence on the angle using [[Cylindrical coordinate system|cylindrical coordinates]] and no dependence on either angle using [[Spherical coordinate system|spherical coordinates]]. The fundamental domain is a [[half-plane]] through the axis, and a radial half-line, respectively. '''Axisymmetric''' and '''axisymmetrical''' are [[adjective]]s which refer to an object having cylindrical symmetry, or '''axisymmetry''' (i.e. rotational symmetry with respect to a central axis) like a [[doughnut]] ([[torus]]). An example of approximate spherical symmetry is the Earth (with respect to density and other physical and chemical properties). In 4D, continuous or discrete rotational symmetry about a plane corresponds to corresponding 2D rotational symmetry in every perpendicular plane, about the point of intersection. An object can also have rotational symmetry about two perpendicular planes, e.g. if it is the [[Cartesian product]] of two rotationally symmetry 2D figures, as in the case of e.g. the [[duocylinder]] and various regular [[duoprism]]s.
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