Quasicrystals were first predicted by Alan Mackay (he knew Penrose and may have been inspired by Penrose tilings)
https://en.wikipedia.org/wiki/Alan_Lindsay_Mackay
I met his son Bob at a climbing gym in Berkeley. http://bobmackay.com/ Bob met Penrose as a teenager through his father and made some of the first computer designs of Penrose tilings.