Quasiperiodic tiling with golden-ratio scaling produces sharp Bragg peaks but no translational symmetry — forbidden 5-fold and 10-fold rotational order.
The Penrose tiling tiles the plane with two shapes obeying a local matching rule; its Fourier transform shows 10-fold symmetric sharp peaks at positions m + n/φ (φ=(1+√5)/2). Shechtman discovered physical quasicrystals (icosahedral Al-Mn) in 1984, earning the 2011 Nobel Prize.