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This letter reports theory of elasticity and hydrodynamics of quasicrystalswith 7-, 14-, 9- and 18-fold symmetries in solid phase, in which the6-dimensional embedding space concept is used. Based on the concept and theLandau-Anderson symmetry breaking principle and the Lubensky hydrodynamics, thegoverning equations for the above quasicrystal systems have been set up, thesolving procedure for the initial-boundary value problems of the equations isdiscussed as well. Though the discussion is concerned only for thequasicrystals, in particular for one of 18-fold symmetry, in solid phase, itmay be a basis for those in soft matter phase observed recently.

Elasticity and hydrodynamics of quasicrystals with 7-, 14-, 9- and 18-fold symmetries