  We analyze the properties of the quasi-one-dimensional triangle lattice
emphasizing the occurrence of flat bands and band touching via the tuning of
the lattice hopping parameters and on-site energies. The spectral properties of
the infinite system will be compared with the transmission through a finite
piece of the lattice with attached semi-infinite leads. Furthermore, we
investigate the adiabatic pumping properties of such a system: depending on the
transmission through the lattice, this results in nonzero integer charge
transfers or transfers that increase linearly with the lattice size.
