The key insight that enabled their explanation was that quasicrystals were, in fact, periodic—but in a higher dimension than ... The original theory by Levine and Steinhardt again explains ...

Electrons moved in two dimensions when influenced by a magnetic field, hinting at how a similar effect would occur in the fourth dimension.

Einstein's theory of general relativity describes how gravity works across the cosmos, suggesting that gravity can impact the three dimensions of space, but also a fourth dimension: time.