In this paper, we show that affine extensions of non-crystallographic Coxetergroups can be derived via Coxeter-Dynkin diagram foldings and projections ofaffine extended versions of the root systems E_8, D_6 and A_4. We show that theinduced affine extensions of the non-crystallographic groups H_4, H_3 and H_2correspond to a distinguished subset of the Kac-Moody-type extensionsconsidered in Dechant et al. This class of extensions was motivated by physicalapplications in icosahedral systems in biology (viruses), physics(quasicrystals) and chemistry (fullerenes). By connecting these here toextensions of E_8, D_6 and A_4, we place them into the broader context ofcrystallographic lattices such as E_8, suggesting their potential forapplications in high energy physics, integrable systems and modular formtheory. By inverting the projection, we make the case for admitting differentnumber fields in the Cartan matrix, which could open up enticing possibilitiesin hyperbolic geometry and rational conformal field theory.
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