This Demonstration shows two simple toy models for the appearance of zero-energy states in a one-dimensional (1D) system such as a simple finite chain of dimers and a two-dimensional (2D) system built from coupled finite chains of dimers. The electronic Hamiltonian matrix is solved in both cases within the tight-binding formalism, where is the hopping matrix element between -type and -type sites, whereas is the hopping matrix element between -type and -type sites within each finite chain. In the 2D case, the inter-chain coupling parameter affects the dispersivity of the electronic bands: if , the bands are almost flat. It was shown in [1] that tuning the ratio introduces anisotropy into the system, therefore inducing a topological transition governing the localization properties at the system edges. Hence, if , there will be no zero energy states, whereas if , edge states appear in the electronic spectra. [2] rationalizes this topological transition in terms of a geometrical phase, the so-called Zak phase, which is equal to in the presence of edge states; otherwise it is zero. The Zak phase is related to another relevant geometric phase (the Berry phase) by contour integration over the first Brillouin zone (see [1] and references therein).