The model shows a surface in which three ridges and three descents meet at a point P such that by a turning about 2pi/3 the surface is transformed into itself. Each normal section through P has a point of inflexion at P and thus its curvature at P is zero. Hence P represents an isolated parabolic umbilical point. Sometimes this surface is called "monkey saddle".

The naming follows the term "Saddle-shaped surface;here however, in contrast to the normal saddle, is space for a third leg - or the tail of a monkey