## Foam Images

https://faculty.math.illinois.edu/~jms

jms@math.uiuc.edu

Back to my other Mathematical Images.

These images show equal-volume, triply periodic foam structures filling space.
The first image shows the Kelvin foam, which uses truncated octahedra
fitting together in the BCC lattice. Surprisingly enough, this turns
out not to be the least-area way to fill space with equal-volume cells.
The second image shows the Weaire-Phelan foam,
which uses two different cell shapes;
this is provably better than the Kelvin foam
(see my paper "Comparing the Weaire-Phelan Equal-Volume Foam to Kelvin's Foam",
[KS2]).
The latter image is also available as a fine-art print.