Polyhedra have fascinated mathematicians and scientists since the time of the ancient Greeks, who regarded them as magical objects. Over the years, several local operations, such as the dual and truncation, have been introduced to create new polyhedra while preserving their symmetries. Notably, an operation known as ambo has been observed to increase the symmetries of self-dual polyhedra.

We investigate the phenomenon of a local symmetry-preserving operation increasing the symmetries of the resulting polyhedron. We show that, for small inflation factors, ambo is the only operation increasing symmetries on the sphere. We conclude showing constructions of families of polyhedra for which ambo or truncation increase symmetries on surfaces of every genus. This is joint work with Gunnar Brinkmann and Heidi Van Den Camp.