double cusp

A point traced out twice as a closed curve is traversed. The maximum number of double points for a nondegenerate quartic curve is three. An ordinary double point is also sometimes known as a node. Aicardi gives pictures of spherical and plane curves with up to five double points, as well as other curves.

crunode | cusp | Gauss's double point theorem | isolated singularity | ordinary double point | quadruple point | rational double point | spinode | tacnode | triple point