Enumerating Regular Mixed-Cell Configurations

By means of the Cayley Trick the problem of enumerating all regular ne mixed subdivisions is reduced to enumerating all regular triangulations. The set of all regular triangulations is well-understood thanks to the bijection with the vertices of the secondary polytope. However, since we are only interested in the conngurations of mixed cells in a mixed subdivision, we want to avoid dealing with other cells. We propose an operator derived from the bistellar ip for regular triangulations to modify a mixed-cell connguration.