Quasicrystal Quanta

The diffraction patterns in Quasicrystals are in geometric series. Their quanta are Dual: Long range, they are digitized by a quasi-Bragg metric; short range, they resonate periodically. The analytic proof exactly matches the numerical discovery and they are experimental confirmed. The structure is hierarchic, icosahedral, and edge-sharing quasi-spherical. The quanta are dual harmonic.