  A remarkable feature of the trimer Su-Schrieffer-Heeger (SSH3) model is that
it supports localized edge states. Although Zak's phase remains quantized for
the case of a mirror-symmetric chain, it is known that it fails to take integer
values in the absence of this symmetry and thus it cannot play the role of a
well-defined bulk invariant in the general case. Attempts to establish a
bulk-edge correspondence have been made via Green's functions or through
extensions to a synthetic dimension. Here we propose a simple alternative for
SSH3, utilizing the previously introduced sublattice Zak's phase, which also
remains valid in the absence of mirror symmetry and for non-commensurate
chains. The defined bulk quantity takes integer values, is gauge invariant, and
can be interpreted as the difference of the number of edge states between a
reference and a target Hamiltonian. Our derivation further predicts the exact
corrections for finite open chains, is straightforwadly generalizable, and
invokes a chiral-like symmetry present in this model.
