Classify crystallographic Coxeter and Kac--Moody structures

Classify the general family of crystallographic Coxeter groups, including the associated infinite Kac--Moody structures, beyond the subclasses already classified.

Background

The thesis relates crystallographic Coxeter-Dynkin diagrams to infinite Kac--Moody algebras and notes that known classifications cover important subclasses, including the hyperbolic cases. However, the full classification of crystallographic Coxeter groups and the corresponding Kac--Moody structures is not complete.

This classification problem is relevant to identifying possible Lorentzian lattices and symmetry groups that could support generalized spacetime quasicrystals.