Hyperbolic paraboloid, made by Fabre de Lagrange, France, 1872. Formed by strings attached to two bars equally spaced, each turns on an arm perpendicular to itself and one arm swings on a pillar; ...

These surfaces are equally "saddle-shaped" at each point. The product of their two curvatures at each point is -1 everywhere. So in a sense they are the opposite (or hyperbolic counterpart) of an ...