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Parallelogram Frameworks and Flexible Quasicrystals

Research output: Contribution to journalJournal articlepeer-review

Forthcoming
<mark>Journal publication date</mark>8/08/2021
<mark>Journal</mark>Mathematical Proceedings of the Royal Irish Academy
Number of pages24
Publication StatusAccepted/In press
<mark>Original language</mark>English

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.