Abstract

A one-dimensional (1D) quasicrystal (QC) is defined as a three-dimensional body which is periodic in the x - y plane and quasiperiodic in the third dimension. Knowing that the possible symmetry operations for a 1D QC are 1, 2, 3, 4, 6, m, (inversion), (horizontal twofold rotation) and (horizontal mirror reflection), 31 possible point groups of 1D QCs have been deduced. These 31 point groups are divided into ten Laue classes and six systems. Considering screw (only ) and glide (only a, b and ) operations, 80 possible space groups of 1D QCs have also been obtained. According to our generalized elasticity theory of QCs, the elastic behaviours, including independent elastic constants and invariants, for each Laue class of 1D QCs have been discussed.

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