This paper describes the synthesis and characterization of a new structurally interesting polybismuthide. The bonding is understood through band structure calculations and a retrotheoretical approach, analyzing the interactions of smaller substructures. Discussion is focused on the Ga-Ga bonding interactions and the weaker Ga-Bi and Bi-Bi interactions within the one-dimensional bismuth ribbons. This is a nice illustration of what a chemist can learn from the band structures of an extended solid and exposes students to an interesting combination of elements in the periodic table that are often overlooked.