Resolution (note: may affect performance) 80; default 80
A general symmetric cubic surface is defined by
$a\sum x_i^3 + b\sum x_i^2 x_j + c\sum x_i x_j x_k$.
While there is no formula in radicals for lines on a general cubic surface, joint work with S. Raman proves the existence of such formulas for $S_4$-symmetric cubic surfaces. This allows us to easily graph the lines by using their exact symbolic formulas!