Decomposing the Secondary Cayley Polytope

The vertices of the secondary polytope of a point connguration correspond to its regular triangulations. The Cayley trick links triangulations of one point connguration, called the Cayley polytope, to the ne mixed subdivisions of a tuple of point conngurations. In this paper we investigate the secondary polytope of this Cayley polytope. Its vertices correspond to all regular mixed subdivisions of a tuple of point conngurations. We demonstrate that it equals the Minkowski sum of polytopes, which we call mixed secondary polytopes, whose vertices correspond to regular-cell conngurations.ondary polytope, bistellar ip. Abstract. The vertices of the secondary polytope of a point connguration correspond to its regular triangulations. The Cayley trick links triangulations of one point connguration, called the Cayley polytope, to the ne mixed subdivisions of a tuple of point conngurations. In this paper we investigate the secondary polytope of this Cayley polytope. Its vertices correspond to all regular mixed subdivisions of a tuple of point conngurations. We demonstrate that it equals the Minkowski sum of polytopes, which we call mixed secondary polytopes, whose vertices correspond to regular-cell conngurations.