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Periodic body-and-bar frameworks. (English) Zbl 1329.52020

Summary: Periodic body-and-bar frameworks are abstractions of crystalline structures made of rigid bodies connected by fixed-length bars and subject to the action of a lattice of translations. We give a Maxwell-Laman characterization for minimally rigid periodic body-and-bar frameworks in terms of their quotient graphs. As a consequence we obtain efficient polynomial time algorithms for their recognition based on matroid partition and pebble games.

MSC:

52C25 Rigidity and flexibility of structures (aspects of discrete geometry)
05B35 Combinatorial aspects of matroids and geometric lattices
74E15 Crystalline structure
68W05 Nonnumerical algorithms
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