Abstract
In this paper the surface-minimizing decompositions of a polyhedron into polyhedra of given volumes is studied. Some corollaries are presented as derivatives of the (local) necessary conditions of optimality, and an overview of the cases when an optimal polyhedral decomposition might exist is also given. An exhaustive classification is given for the case when the polyhedron to be decomposed is convex.
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Heppes, A. On surface-minimizing polyhedral decompositions. Discrete Comput Geom 13, 529–539 (1995). https://doi.org/10.1007/BF02574060
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DOI: https://doi.org/10.1007/BF02574060