Mathematical formulae 
Spiric sections 
A special case of a toric section is the spiric section, in which the intersecting plane is parallel to the rotational symmetry axis of the torus. They were discovered by the ancient Greek geometer Perseus in roughly 150 BC. Well-known examples include the hippopede and the Cassini oval and their relatives, such as the lemniscate of Bernoulli.
Villarceau circles 
Another special case is the Villarceau circles, in which the intersection is a circle despite the lack of any of the obvious sorts of symmetry that would entail a circular cross-section.
General toric sections 
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