  Topological phases of matter have attracted much attention over the years.
Motivated by analogy with photonic lattices, here we examine the edge states of
a one-dimensional trimer lattice in the phases with and without inversion
symmetry protection. In contrast to the Su-Schrieffer-Heeger model, we show
that the edge states in the inversion-symmetry broken phase of the trimer model
turn out to be chiral, i.e., instead of appearing in pairs localized at
opposite edges they can appear at a $\textit{single}$ edge. Interestingly,
these chiral edge states remain robust to large amounts of disorder. In
addition, we use the Zak phase to characterize the emergence of degenerate edge
states in the inversion-symmetric phase of the trimer model. Furthermore, we
capture the essentials of the whole family of trimers through a mapping onto
the commensurate off-diagonal Aubry-Andr\'e-Harper model, which allow us to
establish a direct connection between chiral edge modes in the two models,
including the calculation of Chern numbers. We thus suggest that the chiral
edge modes of the trimer lattice have a topological origin inherited from this
effective mapping. Also, we find a nontrivial connection between the
topological phase transition point in the trimer lattice and the one in its
associated two-dimensional parent system, in agreement with results in the
context of Thouless pumping in photonic lattices.
