The First and Second Most Symmetric Nonsingular Cubic Surfaces

TL;DR

This paper identifies and describes the two most symmetric nonsingular cubic surfaces, providing explicit equations for these highly symmetric algebraic objects.

Contribution

It explicitly characterizes the first and second most symmetric nonsingular cubic surfaces and presents their defining equations.

Findings

x^3+y^3+z^3+t^3=0 is the most symmetric nonsingular cubic surface.

x^2y+y^2z+z^2t+t^2x=0 is the second most symmetric nonsingular cubic surface.

Abstract

The first and second most symmetric nonsingular cubic surfaces are x^3+y^3+z^3+t^3=0 and x^2y+y^2z+z^2t+t^2x=0, respectively.