January 2006

Sextic equations are in general equations of a variable with power terms up to degree 6.

In 3 dimensions the equation contains all the possible terms in x^{n},
y^{n}, z^{n}. In other words the sum over all the terms of the
type shown below where m + n + o <= 6, there are 84 possible combinations
so there are that many constants c_{i}.

Example by Edmond Bonon, rendered in PovRay [sextic.inc]

Other examples of Sextic surfaces (degree 6) are the Barth Sextic, Hunt surface, and Boy surface.