Parallelogram Frameworks and Flexible Quasicrystals

Power, Stephen (2021) Parallelogram Frameworks and Flexible Quasicrystals. Mathematical Proceedings of the Royal Irish Academy, 121A (1). pp. 9-31. ISSN 1393-7197

Text (flexiblequasicrystals_2)
flexiblequasicrystals_2.pdf - Accepted Version
Available under License Creative Commons Attribution.
Download (247kB)

Abstract

The first-order flex space of the bar-joint framework $\G_P$ of a parallelogram tiling $P$ is determined in terms of an explicit free basis. Applications are given to braced parallelogram frameworks and to quasicrystal frameworks associated with multigrids in the sense of de Bruijn and Beenker. In particular we characterise rigid bracing patterns, identify quasicrystal frameworks with finite dimensional flex spaces, and define a zero mode spectrum.