Quasicrystalline three-dimensional foams

We present a numerical study of quasiperiodic foams, in which the bubbles are generated as duals of quasiperiodic Frank-Kasper phases. These foams are investigated as potential candidates to the celebrated Kelvin problem for the partition of three-dimensional space with equal volume bubbles and minimal surface area. Interestingly, one of the computed structures falls close to (but still slightly above) the best known Weaire-Phelan periodic candidate. In addition we find a correlation between the normalized bubble surface area and the root mean squared deviation of the number of faces, giving an additional clue to understanding the main geometrical ingredients driving the Kelvin problem.