# Togliatti Quintic Surface

A **quintic surface** is one defined by a polynomial equation of degree 5. A **nodal surface** is one whose only singularities are **ordinary double points**: that is, points where it looks like the origin of the cone in 3-dimensional space defined by \(x^2 + y^2 = z^2\). A Togliatti surface is a quintic nodal surface with the largest possible number of ordinary double points, namely 31. Here Abdelaziz Nait Merzouk has drawn the real points of a Togliatti surface.