Periodic body-and-bar frameworks
  Abstractions of crystalline materials known as periodic body-and-bar frameworks are made of rigid bodies connected by fixed-length bars and subject to the action of a group of translations. In this paper, we give a Maxwell-Laman characterization for generic minimally rigid periodic body-and-bar frameworks. As a consequence we obtain efficient polynomial time algorithms for their recognition based on matroid partition and pebble games. 
Ciprian S. Borcea, Ileana Streinu and Shin-ichi Tanigawa
math.MG math.CO