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Tiles: 0 | Spots: 0
Quasicrystals
Penrose (1974) discovered aperiodic tilings with 5-fold symmetry — impossible for periodic crystals. Shechtman (1984, Nobel 2011) found real Al-Mn alloys with 10-fold diffraction spots. The tiling is self-similar under inflation by τ=(1+√5)/2 (golden ratio). The diffraction pattern has sharp Bragg peaks (long-range order) but no unit cell — it's a cut through a 6D periodic crystal.
Penrose (1974) discovered aperiodic tilings with 5-fold symmetry — impossible for periodic crystals. Shechtman (1984, Nobel 2011) found real Al-Mn alloys with 10-fold diffraction spots. The tiling is self-similar under inflation by τ=(1+√5)/2 (golden ratio). The diffraction pattern has sharp Bragg peaks (long-range order) but no unit cell — it's a cut through a 6D periodic crystal.