2 equal a_i : dupin berger 20.7.3

The cyclides are the envelopes of spheres (C) the centers of which describe a curve or a surface (G₀) (the deferent) and such that a fixed point O has a constant power p with respect to these spheres (this notion is therefore analogous to that of cyclic curve in the plane).
They are therefore circled surfaces.

The cyclides with a parabola or a paraboloid as a deferent are the spherical cubic surfaces and the cyclides with a conic or a quadric of another kind are the bispherical quartic surfaces, also called "Darboux cyclides".
General equation: . When the deferent is a conic, the cyclide is called "Dupin cyclide".
 

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