  Tight-binding model on a finite chain is studied with four-fold alternated
hopping parameters $t_{1,2,3,4}$. Imposing the open boundary conditions, the
corresponding recursion is solved analytically with special attention paid to
the occurrence of edge states. Corresponding results are strongly corroborated
by numeric calculations. It is shown that in the system there exist four
different edge phases if the number of sites is odd, and eight edges phases if
the chain comprises even number of sites. Phases are labelled by
$\sigma_1\equiv{\rm sgn}(t_1t_3-t_2t_4)$, $\sigma_2\equiv{\rm
sgn}(t_1t_4-t_2t_3)$ and $\sigma_3\equiv{\rm sgn}(t_1t_2-t_3t_4)$. It is shown
that these quantities represent gauge invariant topological indices emerging in
the corresponding infinite chains.

Mesoscale and Nanoscale Physics;High Energy Physics - Theory