Weari-Phelan structure provides a counterexample to Kelvin's conjecture that the minimal area partition of space is realized by an appropriately curved bitruncated cubic honeycomb tesselation. It was discovered by computer simulations of foam in 1993. The problem of finding the minimizing partition is still open, but nowadays you can easily toy with it yourself using Surface Evolver. Who knows, maybe you will discover a better solution!

