Twisted cubic.jpg

(Baker No. 76) Two quadratic surfaces intersecting in a twisted cubic

The two quadratic surfaces are a parabolic cylinder and a hyperbolic paraboloid. This model was constructed by R. P.Baker. In Baker’s catalog, this is called the Cubical Parabola, with the comment: ‘at least two quadrics of the pencil are shown.’ The pencil in question is the pencil (or one-parameter family) of quadratic surfaces obtained by taking linear combinations of the two shown. All the surfaces in the pencil contain the same twisted cubic.