  We study the electronic properties of coupled parallel Polyyne chains in a
couple of symmetric stacking arrangements, namely the AA stacking and the
stacking AB, with the single and triple carbon bonds of one chain aligned (AA)
and anti-aligned (AB) with those of the other chain. Both these arrangements
described by tight binding Hamiltonians, whose parameters are calibrated by
matching low energy dispersion provided by first principle calculations, fall
in the BDI class of topological classification scheme. We calculate the
topological invariants for all the three topological phases of the system: one
for the AA stacking and 2 for the AB one. In the AA stacking, both the
insulating and the metallic phase belongs to the same topological phase.
Whereas, the model exhibits two different values of the topological invariant
in the two different insulating phases (structurally differentiated by
transverse strain). In this later stacking though transition between two
distinct topological phases with the closure of the gap is practically
unachievable due requirement of high amount of transverse strain. We also show
existence of 4 non-zero energy edge modes in the AA stacking and that of 2 zero
energy edge modes in one of the topological phases for the AB stacking.
