Tubular tilings of binary mixtures obey global Euler balance laws that infer hidden-phase topology from the observable phase plus interface geometry, and for d>2 they form a subclass of soft (corner-free) tilings.
Soft tilings
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abstract
By means of constructing a new edge-bending algorithm, we prove that every locally polyhedral tiling of $\mathbb{R}^3$ 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.
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Soft cells, Tubular Tilings and the Hidden Phases in Binary Mixtures
Tubular tilings of binary mixtures obey global Euler balance laws that infer hidden-phase topology from the observable phase plus interface geometry, and for d>2 they form a subclass of soft (corner-free) tilings.