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Quasicrystals seem to exist in a state somewhere between glass (disordered atoms) and crystals (ordered atoms) and show qualities of symmetry that were thought impossible.

Quasicrystals – [bbc.co.uk]

Quasicrystals are interesting quirks of solid-state physics. It used to be thought that the atoms in solid materials1 were either totally ordered (crystalline) or totally disordered (glasses), but those in quasicrystals are neither. Unlike normal crystals, quasicrystals show order only on a small scale, but, by the same token, the order that does exist can produce large-scale effects.

‘Impossibly Perfect’ Crystals Found in Nature – [discovery.com]

Like crystals, quasicrystals have specific shapes that repeat again and again. For crystals there is only one shape (diamond, cube, etc.) that gives a crystal up to six different symmetries. Quasicrystals, on the other hand, have two or more different shapes that repeat but with different spaces in between, giving them beautiful and intricate patterns that are perfectly symmetrical in five, seven, even 12 different dimensions. This high level of symmetry is traditionally forbidden for crystals.

Unlike traditional crystals, however, quasicrystals actually have two geometric structures which enable them to have incredibly complex and often beautiful structures that are symmetrical in five, seven, or even 12 dimensions.

Quasicrystal – [absoluteastronomy.com]

Quasicrystals – [jcrystal.com]

5-fold Crystal Symmetry

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