  We extend our generic rigidity theory for periodic frameworks in the plane to
frameworks with a broader class of crystallographic symmetry. Along the way we
introduce a new class of combinatorial matroids and associated linear
representation results that may be interesting in their own right. The same
techniques immediately yield a Maxwell-Laman-type combinatorial
characterization for frameworks embedded in 2-dimensional cones that arise as
quotients of the plane by a finite order rotation.
