We have resolved long-standing discrepancies between the theoretical and experimental crystal structures of boron carbide B 13 C 2 . Theoretical studies predict that B 13 C 2 should be stoichiometric and have the highest symmetry of the boron carbides. Experimentally, B 13 C 2 is a semiconductor and many defect states have been reported, particularly in the CBC chain. Reconciling the disordered states of the chain, the chemical composition, and the lowest-energy state is problematic. We have solved this problem by constructing a structural model where approximately three-quarters of the unit cells contain (B 11 C)(CBC) and one-quarter of them contain (B 12 ) (B 4 ). This structural model explains many experimental results, such as the large thermal factors in x-ray diffraction and the broadening of the Raman spectra, without introducing unstable CBB chains. The model also solves the energy-gap problem. We show that there are many arrangements of these two types of unit cells, which are energetically almost degenerate. This demonstrates that boron carbides are well described by a geometrically frustrated system, similar to that proposed for β-rhombohedral boron.