  Maxwell lattices are characterized by an equal number of degrees of freedom
and constraints. A subset of them, dubbed topological lattices, are capable of
localizing stress and deformation on opposing edges, displaying a polarized
mechanical response protected by the reciprocal-space topology of their band
structure. In two dimensions, the opportunities for topological polarization
have been largely restricted to the kagome and square lattice benchmark
configurations, due to the non-triviality of generating arbitrary geometries
that abide by Maxwell conditions. In this work, we introduce a generalized
family of augmented topological lattices that display full in-plane topological
polarization. We explore the robustness of such polarization upon selection of
different augmentation criteria, with special emphasis on augmented
configurations that display dichotomous behavior with respect to their
primitive counterparts. We corroborate our results via intuitive table-top
experiments conducted on a lattice prototype assembled from 3D-printed
mechanical links.
