  The interaction of spin-polarized one-dimensional (1D) topological edge modes
localized along single-atomic steps of the topological crystalline insulator
$Pb_{0.7}Sn_{0.3}Se(001)$ has been studied systematically by scanning tunneling
spectroscopy. Our results reveal that the coupling of adjacent edge modes sets
in at a step{to{step distance $d_{ss} < 25$ nm, resulting in a characteristic
splitting of a single peak at the Dirac point in tunneling spectra. Whereas the
energy splitting exponentially increases with decreasing $d_{ss}$ for
single-atomic steps running almost parallel, we find no splitting for
single-atomic step edges under an angle of $90^{o}$. The results are discussed
in terms of overlapping wave functions with $p_x; p_y$ orbital character.
