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quasicrystals
Unusual atomic crystal arrangements including 5, 8 and 12-fold symmetries found in aluminum alloys & certain polymers

5, 8, 10, 12
Symmetries quasicrystals include.

2, 4, 6
The usual symmetry types found in crystallography.

nobel peace prize
Dan Schectman made electron microscopic observations of quasicrystals and won this for his discovery of them.

polygonal and icosahedral
The two known quasicrystal types.

penrose tiles
A geometric relationship used in approximately modeling quasicrystals, although their original creation wasn't to describe them.

space
Penrose Tiles are small non-identical shapes arranged to fill this completely.

phi
Penrose tiles give us a geometric representation of quasicrystal molecules and atoms and are made up of this.
islamic
Strong evidence reveals that these mathematicians and artists discovered quasicrystalline properties of "Penrose tilings" hundreds of years before Kepler.

razor blades
One of the many uses for quasicrystals.
