  Mass-spring networks (MSNs) have long been used as approximate descriptions
of many biological and engineered systems, from actomyosin networks to
mechanical trusses. In the last decade, MSNs have re-attracted theoretical
interest as models for phononic metamaterials with exotic properties such as
negative Poisson's ratio, negative effective mass, or gapped vibrational
spectra. A practical advantage of MSNs is their tuneability, which allows the
inverse design of materials with pre-specified bandgaps. Building on this fact,
we demonstrate here that designed MSNs, when subjected to Coriolis forces, can
host topologically protected chiral edge modes at predetermined frequencies,
thus enabling robust unidirectional transmission of mechanical waves. Similar
to other recently discovered topological materials, the topological phases of
MSNs can be classified by a Chern invariant related to time-reversal symmetry
breaking.
