Ultrarigid periodic frameworks

Abstract

We give an algebraic characterization of when a $d$-dimensional periodic framework has no non-trivial, symmetry preserving, motion for any choice of periodicity lattice. Our condition is decidable, and we provide a simple algorithm that does not require complicated algebraic computations. In dimension $d=2$, we give a combinatorial characterization in the special case when the the number of edge orbits is the minimum possible for ultrarigidity. All our results apply to a fully flexible, fixed area, or fixed periodicity lattice.

arXiv comment34 pages, 3 figures (v4, updated references and discussion, author contact data)

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Cited by in corpus (2)

• The first-order flexibility of a crystal framework
• Flexible placements of periodic graphs in the plane