  Systems as diverse as mechanical structures assembled from elastic
components, and photonic metamaterials enjoy a common geometrical feature: a
sublattice symmetry. This property realizes a chiral symmetry first introduced
to characterize a number of electronic insulators in the vicinity of their
energy gaps. In this article, we introduce a generic framework to elucidate and
design zero-energy topological boundary modes in all systems enjoying a chiral
symmetry, whether crystalline or amorphous. We first show how to distinguish
chiral insulators from one another by a real-space measure: their chiral
polarization. In crystals, we use it to redefine the very concept of
bulk-boundary correspondence, and resolve long-standing ambiguities in its
application to chiral insulators. In amorphous metamaterials, we use it to lay
out generic geometrical rules to locate topologically distinct phases, and
explain how to engineer localized zero-mode wave guides even more robust than
in periodic structures.
