The Feb issue of AMS Notices (American Mathematical Society) contains an article of possible interest to crystallographers.
http://www.ams.org/notices/200802/ "Crystals That Nature Might Miss Creating" - Toshikazu Sunada I confess myself perplexed as to what is actually being described in this article. In particular, I cannot figure out whether the "K_4 lattice" being described is truly a lattice in the sense that crystallographers understand the term. If so then what does it correspond to in our usual nomenclature? -- Ethan A Merritt