Parallelogram frameworks and flexible quasicrystals
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.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2021
- DOI:
- 10.48550/arXiv.2107.06602
- arXiv:
- arXiv:2107.06602
- Bibcode:
- 2021arXiv210706602P
- Keywords:
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- Mathematics - Metric Geometry;
- 52C25;
- 52C23
- E-Print:
- 20 pages, 8 figures. Minor corrections and clarifications have been made