Schl?fli already classified all real cubic surfaces with respect to the singularities occurring on them in 1863. Kn?rrer/Miller gave a more rigorous classification in 1987.

In this section, we give equations and images for all of their 45 types which only have rational double points as singularities. The example on the left has one A₁ and one A₅ singularity.

In our gallery the lines on the cubic surfaces are colored according to their multiplicity.
This is particularly interesting when looking at an animation which shows the deformation of one type of cubic surfaces into another (see e.g. the deformations of the four-nodal Cayley cubic).

>>> Go to the gallery!