  Combinatorial characterisations are obtained of symmetric and anti-symmetric
infinitesimal rigidity for two-dimensional frameworks with reflectional
symmetry in the case of norms where the unit ball is a quadrilateral and where
the reflection acts freely on the vertex set. At the framework level, these
characterisations are given in terms of induced monochrome subgraph
decompositions, and at the graph level they are given in terms of sparsity
counts and recursive construction sequences for the corresponding signed
quotient graphs.
