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

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Authors: Fabrice Delbary
Cited by: 0

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 $3$ (in order to fulfill Plateau's laws): the tetrahedron, the cube, the dodecahedron. The clusters respectively contain a bubble of genus $3, 5, 11$. The construction is quite generic and can be used with any convex polyhedron. If stable, the cluster obtained using a polyhedron with $n$ faces has $3n+2$ bubbles and one of these bubbles has genus $n-1$. 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.

Fields of Study & Subjects

Geometric Analysis and Curvature Flows Fluid Dynamics and Heat Transfer Computational Geometry and Mesh Generation

Publication details

Journal / source
arXiv (Cornell University)
Publication date
31 January 2026
Language
EN
Document type
Preprint