In 1887, Lord Kelvin conjectured that a honeycomb of truncated tetrahedra would partition space into cells of equal volume with the least surface area. The faces of
the truncated octahedra are curved slightly in order to meet at the proper soap film angles. The conjecture has now been overthrown. Denis Weaire and Robert Phelan have found a froth whose surface area is 0.3% less
than Kelvin's. This structure, shown above, uses two kinds of cells, a dodecahedron and a tetrakaidecahedron, which has two hexagonal and twelve pentagonal faces.
The above animation shows the honeycomb of truncated octahedra.
Text and animations by Nick Mee from the CD-ROMS POLYTOPIA I: Tessellations and Polyhedra and POLYTOPIA II: Honeycombs and Polytopes -
Published by Virtual Image