Cubic Surfaces belong to the most classical Math Models. The Clebsch Diagonal Surface even made it to the 1892 Chicago World Fair. Knörrer and Miller classified cubic surfaces in a modern way in the 1980s, and found essentially 45 different types apart from some other more special types.
Every non-ruled cubic contains a certain number of straight lines (27 or less).
For each of the 45 types, we produced one example which shows all real lines contained in the surface.
The example shown here is number 42.
See also: MO-Labs.com.