English

Combinatorial Polytope Enumeration

Combinatorics 2009-08-13 v1

Abstract

We describe a provably complete algorithm for the generation of a tight, possibly exact superset of all combinatorially distinct simple n-facet polytopes in R^d, along with their graphs, f-vectors, and face lattices. The technique applies repeated cutting planes and planar sweeps to a d-simplex. Our generator has implications for several outstanding problems in polytope theory, including conjectures about the number of distinct polytopes, the edge expansion of polytopal graphs, and the d-step conjecture.

Keywords

Cite

@article{arxiv.0908.1619,
  title  = {Combinatorial Polytope Enumeration},
  author = {Sandeep Koranne and Anand Kulkarni},
  journal= {arXiv preprint arXiv:0908.1619},
  year   = {2009}
}
R2 v1 2026-06-21T13:34:38.476Z