Totally Splittable Polytopes
Sven Herrmann, Michael Joswig
TL;DR
This paper provides a complete classification of totally splittable polytopes, which are polytopes where every triangulation can be refined from splits, enhancing understanding of their geometric structure.
Contribution
It offers the first comprehensive classification of totally splittable polytopes, clarifying their properties and significance in polyhedral geometry.
Findings
Complete classification of totally splittable polytopes
Characterization of splits and triangulations in these polytopes
Insights into the structure of polytopes with split-based triangulations
Abstract
A split of a polytope is a (necessarily regular) subdivision with exactly two maximal cells. A polytope is totally splittable if each triangulation (without additional vertices) is a common refinement of splits. This paper establishes a complete classification of the totally splittable polytopes.
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