Enumerating Regular Mixed-Cell Configurations

By means of the Cayley Trick the problem of enumerating all regular fine 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 configurations of mixed cells in a mixed subdivision, we want to avoid dealing with other cells. We propose an operator derived from the bistellar flip for regular triangulations to modify a mixed-cell configuration. Received June 30, 1997, and in revised form December 1, 1997.