  We investigate the spectral properties of a quasi-one-dimensional lattice in
two possible dimerisation configurations. Both configurations are characterized
by the same lattice topology and the identical spectra containing a flat band
at zero energy. We find that one of the dimerised configuration has similar
symmetry to a one-dimensional chain proposed by Su-Schrieffer-Heeger for
studying solitons in conjugated polymers. Whereas, the other dimerised
configuration only shows non-trivial topological properties in the presence of
chiral-symmetry breaking adiabatic pumping.
