  Mechanical metamaterials present a promising platform for seemingly
impossible mechanics. They often require incompatibility of their elementary
building blocks, yet a comprehensive understanding of its role remains elusive.
Relying on an analogy to ferromagnetic and antiferromagnetic binary spin
interactions, we present a universal approach to identify and analyze
topological mechanical defects for arbitrary building blocks. We underline
differences between two- and three-dimensional metamaterials, and show how
topological defects can steer stresses and strains in a controlled and
non-trivial manner and can inspire the design of materials with hitherto
unknown complex mechanical response.
