Enumerating regular mixed-cell configurations

By means of the Cayley Trick the problem of enumerating all regular fine mi xed subdivisions is reduced to enumerating all regular triangulations. The set of all regular triangulations is well understood thanks to the bijectio n with the vertices of the secondary polytope. However, since we are only i nterested in the configurations of mixed cells in a mixed subdivision, we w ant to avoid dealing with other cells. We propose an operator derived from the bistellar flip for regular triangulations to modify a mixed-cell config uration.