Fermat cubic

In geometry, the Fermat cubic, named after Pierre de Fermat, is a surface defined by
Methods of algebraic geometry provide the following parameterization of Fermat's cubic:
In projective space the Fermat cubic is given by
The 27 lines lying on the Fermat cubic are easy to describe explicitly: they are the 9 lines of the form ("w" : "aw" : "y" : "by") where "a" and "b" are fixed numbers with cube −1, and their 18 conjugates under permutations of coordinates.