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Dupin cyclide

Dupin cyclide
Image credit: Robert March
Dupin cyclide is the envelope of all spheres touching three given fixed spheres. (Each of the fixed spheres is to be touched in an assigned manner, either externally or internally.) Equivalently, the envelope of all spheres whose centers lie on a given conic section and which touch a given sphere. Also equivalently, the inverse of a torus.

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