Abstract
A mean-field theory for the geometry and diffusive growth rate of
soap bubbles in dry 3D foams is presented. Idealized foam cells
called isotropic Plateau polyhedra (IPPs), with F identical
spherical-cap faces, are introduced. The geometric properties
(e.g., surface area S, curvature R, edge length L,
volume V) and growth rate 
of the cells are
obtained as analytical functions of F, the sole variable. IPPs
accurately represent average foam bubble geometry for arbitrary
F ⩾ 4, even though they are only constructible for F = 4,6,12. While R/V1/3, L/V1/3 and exhibit
F1/2 behavior, the specific surface area S/V2/3 is
virtually independent of F. The results are contrasted with
those for convex isotropic polyhedra with flat faces.