Flexible-lattice extensions for crystallographic body-bar and body-hinge frameworks

Establish characterizations of symmetry-forced generic rigidity for crystallographic body-bar frameworks with flexible lattice representations and for periodic body-hinge or molecular frameworks.

Background

For body-bar frameworks in d-space with a fixed lattice representation, the paper cites a complete characterization for all crystallographic groups. It explicitly identifies as unresolved the extension of that result to flexible lattice representations, as well as analogous results for periodic body-hinge and molecular frameworks.