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

TL;DR

This paper explores the construction of stable soap bubble clusters with multiple torus bubbles using geometric configurations based on Platonic solids, prisms, and Archimedean solids, extending previous work to more complex shapes.

Contribution

It introduces new geometric methods for creating stable soap bubble clusters with multiple torus bubbles beyond Platonic solids, including prisms and Archimedean solids.

Findings

Stable clusters can be constructed with various polyhedral geometries.

The clusters contain bubbles with genus related to the number of faces.

The construction method is quite general and adaptable.

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.