A cyclide is a pair of focal conics which are the envelopes of two one-parameter families of spheres, sometimes also called a cyclid. The cyclide is a quartic surface, and the lines of curvature on a cyclide are all straight lines or circular arcs. The standard tori and their inversions in an inversion sphere S centered at a point x_0 and of radius r, given by I(x_0, r) = x_0 + ((x - x_0) r^2)/( left bracketing bar x - x_0 right bracketing bar )^2, are both cyclides. Illustrated above are ring cyclides, horn cyclides, and spindle cyclides. The figures on the right correspond to x_0 lying on the torus itself, and are called the parabolic ring cyclide, parabolic horn cyclide, and parabolic spindle cyclide, respectively.
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