Extremal properties for dissections of convex 3-polytopes
Combinatorics
2013-04-30 v1 Metric Geometry
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.
Keywords
Cite
@article{arxiv.math/0012169,
title = {Extremal properties for dissections of convex 3-polytopes},
author = {Jesús A. De Loera and Francisco Santos and Fumihiko Takeuchi},
journal= {arXiv preprint arXiv:math/0012169},
year = {2013}
}
Comments
19 pages