Soft tilings
Abstract
By means of constructing a new edge-bending algorithm, we prove that every locally polyhedral tiling of R3 can be completely softened. A weaker form of this statement, for polyhedral space tilings, was conjectured by Domokos, Goriely, G. Horv\'ath and Regos in 2024. We also provide a short proof for a result of Domokos, G. Horv\'ath, and Regos, stating that in a balanced polygonic tiling of the plane, the average number of spikes is at least 2 per cell.
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