Natural tilings and the geometry of soft cells.

9^th December 2025, 14:00
Gábor Domokos
Budapest University of Technology and Economics, Hungary

Abstract

I will describe a new class of shapes, called soft cells, which tile space without gaps and overlaps while they also minimize the number of sharp corners [1]. In the Euclidean plane, for periodic tilings this minimum is 2 while in the 3D Euclidean space we find monotiles without any sharp corners.
I will explain how these soft tilings can be generated from polyhedral tilings by suitable bending of edges and I will also explain how they are related to triply perioidic minimal surfaces and also the Kelvin foam [2].
In nature we encounter soft cells on many scales, ranging from material nanostructure of polymers to macroscopic patterns in geological shear zones. I will describe some of these applications.
[1] G. Domokos, A. Goriely, Á. G. Horváth, and K. Reg?s. Soft cells and the geometry of seashells. PNAS Nexus, 3(9):pgae311, 2024. doi: 10.1093/pnas-nexus/pgae311.
[2] G. Domokos, A. Goriely, Á. G. Horváth, and K. Reg?s. Soft cells, Kelvin's foam and the minimal surfaces of Schwarz. https://arxiv.org/abs/2412.04491.