The pyramidal growth
Combinatorics
2022-04-22 v3 Metric Geometry
Abstract
Can one build an arbitrary polytope from any polytope inside by iteratively stacking pyramids onto facets, without losing the convexity throughout the process? We prove that this is indeed possible for (i) 3-polytopes, (ii) 4-polytopes under a certain infinitesimal quasi-pyramidal relaxation, and (iii) all dimensions asymptotically. The motivation partly comes from our study of K-theory of monoid rings and of certain posets of discrete-convex objects.
Keywords
Cite
@article{arxiv.2002.08520,
title = {The pyramidal growth},
author = {Joseph Gubeladze},
journal= {arXiv preprint arXiv:2002.08520},
year = {2022}
}
Comments
New Section 3 (Outline of the proof) and figures added