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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