Their intricate, star-like patterns have influenced architecture and art, echoing designs found in medieval Islamic Girih tiles , which unknowingly used quasicrystalline geometry 500 years before Western science "discovered" it.
Because their atomic structure is so densely packed and lacks the "cleavage planes" of normal crystals, quasicrystals possess unique physical properties: Quasicrystals and Geometry
They are used as coatings for non-stick frying pans and surgical tools. Maintains a specific "long-range" order
They are poor conductors of heat and electricity compared to normal metals, making them excellent thermal barriers. making them excellent thermal barriers.
The geometric foundation of quasicrystals was actually discovered in pure mathematics before it was found in nature. In the 1970s, Roger Penrose created . By using just two different diamond-shaped tiles, he proved it was possible to cover an infinite plane in a pattern that: Never repeats (aperiodic). Maintains a specific "long-range" order. Relies on the Golden Ratio ( ) to determine the frequency and placement of the tiles.
For example, a 1D Fibonacci sequence (a simple quasicrystal model) can be created by projecting points from a 2D square grid at a specific "irrational" angle. Similarly, the complex 3D structures we see in aluminum-manganese alloys are often viewed as "shadows" or slices of a 6-dimensional regular lattice. 4. Real-World Applications