Soft tilings
Metric Geometry
2026-04-21 v1 Combinatorics
Geometric Topology
Abstract
By means of constructing a new edge-bending algorithm, we prove that every locally polyhedral tiling of can be completely softened. A weaker form of this statement, for polyhedral space tilings, was conjectured by Domokos, Goriely, G. Horv\'ath and Reg\H{o}s in 2024. We also provide a short proof for a result of Domokos, G. Horv\'ath, and Reg\H{o}s, stating that in a balanced polygonic tiling of the plane, the average number of spikes is at least 2 per cell.
Keywords
Cite
@article{arxiv.2604.18545,
title = {Soft tilings},
author = {Gergely Ambrus and Dorottya Dancsó},
journal= {arXiv preprint arXiv:2604.18545},
year = {2026}
}