What decides if a Coxeter Group is "crystalline" or "non-crystalline"? I am currently writing a research essay concerning Crystallographic theories applied to Virology. Do keep in mind that I am not a mathematician and I know very little about Coxeter groups in general. Please bear with me; I'm trying. 
One of my sources,"Mathematical Virology: a novel approach to the structure and assembly of viruses" (Twarock 2006), draws a connection between the "six-dimensional root lattice 6D and the non-crystallographic Coxeter group H3". According to the paper, Twarock was able to use H3, and it's affine extension, to infer generalized lattices of the capsid structure. 
What distinct a 'non-crystallographic' Coxeter group from a 'crystallographic' one? 
Also, I believe "affine extension" to be an extension of an object that preserves the parallel relationship of its parts, sort of a scaling thing. Is this true? 
And is it correct to assume that Coxeter Groups are part of Group Theory?
Thank you so much! 
P.S. If anyone knows anything about what exactly a "six-dimensional root lattice 6D" entails, I'd be thrilled to find out. 

Nobody has really answered the question in the title. The answer to that question: the group is crystallographic if and only if all the entries in the Coxeter matrix are $1,2,3,4,6$ or $\infty$.
