Quasicrystals are based on the symmetry system of the icosahedron/dodecahedron, in which it it is impossible to periodically tile space. “Proper” crystal struc

Quasicrystals are based on the symmetry system of the icosahedron/dodecahedron, in which it it is impossible to periodically tile space. “Proper” crystal structures are periodic, and are not necessarily related to any Platonic solid. See https://en.wikipedia.org/wiki/Crystal_system https://en.wikipedia.org/wiki/Crystal_system (but I’m not quite sure where the 5 comes from in TFA).