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Extremal properties for dissections of convex 3-polytopes

Jesús A. De Loera·Francisco Santos·Fumihiko Takeuchi
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Abstract

A dissection of a convex d-polytope is a partition of the polytope into d-simplices whose vertices are among the vertices of the polytope. Triangulations are dissections that have the additional property that the set of all its simplices forms a simplicial complex. The size of a dissection is the number of d-simplices it contains. This paper compares triangulations of maximal size with dissections of maximal size. We also exhibit lower and upper bounds for the size of dissections of a 3-polytope and analyze extremal size triangulations for specific non-simplicial polytopes: prisms, antiprisms, Archimedean solids, and combinatorial d-cubes.

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Jesús A. De Loera, Francisco Santos, Fumihiko Takeuchi. 2000-12-18. Extremal properties for dissections of convex 3-polytopes. https://doi.org/10.1137/s0895480199366238

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