Abstract.
The vertices of the secondary polytope of a point configuration correspond to its regular triangulations. The Cayley trick links triangulations of one point configuration, called the Cayley polytope, to the fine mixed subdivisions of a tuple of point configurations. 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 configurations. We demonstrate that it equals the Minkowski sum of polytopes, which we call mixed secondary polytopes, whose vertices correspond to regular-cell configurations.
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Received October 1, 1998, and in revised form July 23, 1999.
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Michiels, T., Cools, R. Decomposing the Secondary Cayley Polytope . Discrete Comput Geom 23, 367–380 (2000). https://doi.org/10.1007/PL00009506
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DOI: https://doi.org/10.1007/PL00009506