  We provide a variational construction of special solutions to the generalized
surface quasi-geostrophic equations. These solutions take the form of N vortex
patches with N-fold symmetry , which are steady in a uniformly rotating frame.
Moreover, we investigate their asymptotic properties when the size of the
corresponding patches vanishes. In this limit, we prove these solutions to be a
desingularization of N Dirac masses with the same intensity, located on the N
vertices of a regular polygon rotating at a constant angular velocity.
