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Stable soap bubble clusters with multiple torus bubbles: getting a bit more exotic

Popular Physics 2026-03-20 v2 Soft Condensed Matter

Abstract

Recently, numerical examples of stable soap bubble clusters with multiple torus bubbles have been presented. The geometry of these clusters is based on the Platonic solids whose vertices have valence 33 (in order to fulfill Plateau's laws): the tetrahedron, the cube, the dodecahedron. The clusters respectively contain a bubble of genus 3,5,113, 5, 11. The construction is quite generic and can be used with any convex polyhedron. If stable, the cluster obtained using a polyhedron with nn faces has 3n+23n+2 bubbles and one of these bubbles has genus n1n-1. We propose here to show that is it possible to get stable soap bubble clusters with multiple torus bubbles using a geometry based on prisms and Archimedean solids as well.

Cite

@article{arxiv.2602.02580,
  title  = {Stable soap bubble clusters with multiple torus bubbles: getting a bit more exotic},
  author = {Delbary Fabrice},
  journal= {arXiv preprint arXiv:2602.02580},
  year   = {2026}
}
R2 v1 2026-07-01T09:32:41.670Z