Confocal quadrics

The surface consists of three surfaces (ellipsoid , one-sheeted and two-sheeted hyperboloid) chosen from a family of confocal quadrics. The three surfaces cut each other orthogonally and the curve of intersecton of any two surfaces of them is a line of curvature on both surfaces.

Spindle cyclide

Spindle cyclide arises by an inversion from a spindle torus.

Ring cyclide

The cyclides of Dupin are characterized by the property that all their lines of curvature are pieces of circles or straight lines. Ring cyclide arises by an inversion from a ring torus.

Ring cyclide2

The cyclides of Dupin are characterized by the property that all their lines of curvature are pieces of circles or straight lines. Ring cyclide arises by an inversion from a ring torus.