On Teissier's example of an equisingularity class that cannot be defined over the rationals

A result of Teissier says that the cone over one of classical polygon examples in the real projective space gives, by complexification, a surface singularity which is not Whitney equisingular to a singularity defined over the field of rational numbers Q. In this note we correct the example and give a complete proof of Tesissier’s result.