Cyclide

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 (Pinkall 1986). The standard tori and their inversions in an inversion sphere centered at a point and of radius , given by

are both cyclides (Pinkall 1986). Illustrated above are ring cyclides, horn cyclides, and spindle cyclides. The figures on the right correspond to lying on the torus itself, and are called the parabolic ring cyclide, parabolic horn cyclide, and parabolic spindle cyclide, respectively.