Quasicrystals are materials that have long-range atomic order but lack the translational symmetry of conventional crystals. All quasicrystalline tilings and packings I have read about thus far, whilst lacking translational symmetry, have rotation axes and reflection planes. I'm wondering if anyone is aware of experimental evidence of quasicrystals which lack reflection symmetry (and thus possess implicit chirality), or can provide a theoretical rationale for why such structures can or cannot exist.
To clarify, a cursory google search turns up a paper interpreting a viral capsid as having chiral quasicrystalline order - Whilst I don't have access to the paper, I specifically exclude this sort of intepretation from consideration as I'm talking about structures with potentially infinite spatial extent, which viruses do not have.