A four-sided quadrilateral not contained in a plane. The lines connecting the midpoints of opposite sides of a skew quadrilateral intersect (and bisect) each other. The problem of finding the minimum bounding surface of a skew quadrilateral was solved by Schwarz in terms of Abelian integrals and has the shape of a saddle. It is given by solving (1 + f_y^2) f_(x x) - 2f_x f_y f_(x y) + (1 + f_x^2) f_(y y) = 0.

hyperbolic paraboloid | quadrilateral | skew polygon