2000 character limit reached
The pyramidal growth (2002.08520v3)
Published 20 Feb 2020 in math.CO and math.MG
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.