Combinatorics of flag simplicial 3-polytopes
Combinatorics
2013-01-22 v2 Metric Geometry
Abstract
In the focus of this paper is the operation of edge contraction. One can show that simplicial 3-polytope is flag iff contraction of any its edge gives simplicial 3-polytope. Our main result states that any flag simplicial 3-polytope can be reduced to octahedron by sequence of edge contractions. Using this operation we introduce a partial order on the set of flag simplicial 3-polytopes and study Hasse graph of corresponding poset. We estimate input and output degrees of vertices of this Hasse graph.
Keywords
Cite
@article{arxiv.1212.4696,
title = {Combinatorics of flag simplicial 3-polytopes},
author = {Vadim Volodin},
journal= {arXiv preprint arXiv:1212.4696},
year = {2013}
}