A superellipse is a Lamé curve, described by the formula |x/a|n + |y/b|n = 1, for which n > 2. Superellipses have a form partway between an ellipse and a rounded rectangle (or, if a = b, partway between a circle and a rounded square).


The Danish poet and architect Piet Hein decided that the superellipse with n = 5/2 and a/b = 6/5 is the most pleasing the eye. This so-called Piet Hein ellipse was quickly adopted as the basic motif for planning an open space at the center of Stockholm and was also incorporated into Scandinavian designs for office tables, desks, beds, and even roundabouts in roads.


The surface of revolution of a superellipse is a superellipsoid, one special form of which has been nicknamed the superegg.