A researcher from the University of Bath has found a new approach to an old geometric problem of modelling the most efficient way of packing shapes to form a foam. The discovery is not only making waves in the mathematical world, but could also lead to medical advances in creating hip replacements and replacement bone tissue for bone cancer patients. The 'Kelvin problem,' posed by Lord Kelvin in 1887, was to find the most efficient way of splitting space into cells of equal volume with the least area of surface between them. Kelvin's solution to the problem was a honeycomb of truncated octahedrons - shapes with six square faces and eight hexagonal faces. A better solution was devised by physicists Weaire and Phelan at Trinity College Dublin who created a honeycomb structure which inspired the striking architecture of the Water Cube aquatic centre that featured in the 2008 Beijing Olympics. The Weaire-Phelan structure is composed of two different shapes: an irregular pentagonal dodecahedron (12-faced polyhedron) and a polyhedron with 14 faces.