Quartic Surfaces

A "quartic surface" (or a "surface of order four") is defined by the vanishing of a degree four (with highest exponent four) polynomial. We have fewer of these models than cubics, which is in part because there are far too many quartics for a classification such as with the cubics to be practical. Nonetheless, there are some quartic surfaces with very interesting properties to explore. See this Wolfram Mathworld page for a list of interesting quartics.