Roland Piquepaille writes "Why are diamonds so shiny and beautiful? A Japanese mathematician says it's because of their unique crystal structure and two key properties, called 'maximal symmetry' and 'strong isotropic property.' According to the American Mathematical Society (AMS), he found that out of all the crystals that are possible to construct mathematically, just one shares these two properties with the diamond. So far, his K4 crystal exists only as a mathematical object. And nobody knows if it exists — or if it can be synthesized."