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The geometry of soft cells is more important than previously suspected
2026. 05. 19.
BME researchers have found that their recently discovered shape class can be used to describe models of both living and inanimate microstructures.
A year and a half ago, a publication by BME researchers on the discovery of soft cells, shapes that fill space perfectly without vertices, caused a stir in the international scientific world. Gábor Domokos, Krisztina Regős (Faculty of Architecture, Department of Morphology and Geometric Modelling), Ákos G. Horváth (Faculty of Natural Sciences, Department of Algebra and Geometry) and Alain Goriely (University of Oxford, Institute of Mathematics) have come to the recognition of the properties of the universal geometric shape class by studying naturally occurring shapes.
The four researchers have now published a new study in the Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (PRSA), published by the Royal Society, the British Academy of Sciences. The article “Soft cells, Kelvin foam and the minimal surfaces of Schwarz” (Lágy cellák, Kelvin-hab és a Schwarz-féle minimálfelületek) shows that
spatial soft cells may occupy a much more important place in the description of living and inanimate nature than previously thought.
The authors reveal a surprising derived connection between soft cells and the most important geometric models of material microstructure, which are fundamental tools for describing living organisms (such as the butterfly wing), foams (including simple soap foam), and even plastics (for example, multi-component polymers).
"The complex, gyroid-like patterns, the famous model of the Kelvin foam and the classical triply periodic minimal surfaces can all be connected through the geometric concept of soft cells," Gábor Domokos told bme.hu.
The researchers have also succeeded in formulating a possible model of the phase transitions observed in the structure of polymers in recent years by physicists, with the aid of soft cells. Although the article relies strictly on analytical tools, it nevertheless connects the geometry of soft cells with a great many biological and physical phenomena.
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