What is a circle classified as?

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A circle is not a polygon because it is not solely comprised of line segments. If this is true, then what is a circle classified as? Is there a group of shapes that includes shapes with curves?

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It is a simple closed curve, or a Jordan curve, which is just a nice loop in the plane. If you talk about symmetry properties, you can separate it from that large category. It is a smooth curve because it is differentiable, unlike the Twitter logo. It is also a 1-sphere because it is one dimensional and consists of all the points within a plane that are a given distance from a center.

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'Conic sections' ? This includes hyperbolae, parabolae and ellipses (circle is a special case of ellipse).