Comment by mswphd

Crystals are a form of solid that in some sense have "long range regularity". One way (the obvious way) to have this is to have a (translational) symmetry. For a while, it was thought this was the only way. Aperiodicity (in the sense of this post) was then discovered, leading to the discovery of a new way to arrange matter that maintains this "long range regularity" without having translational symmetry, namely quasi-crystals. This was the basis of the 2011 Nobel Prize in Chemistry.

For a popular exposition on quasi-crystals you can see

https://www.quantamagazine.org/quasicrystals-spill-secrets-o...