We investigate the thermodynamic stability of carbon-rich icosahedral boron carbide at different compositions, ranging from to , using first-principles calculations. Apart from , generally addressed in the literature, , represented by (C-C), where and (C-C) denote a carbon atom occupying the polar site of the icosahedral cluster and a diatomic carbon chain, respectively, is predicted to be thermodynamically stable under high pressures with respect to as well as pure boron and carbon phases. The thermodynamic stability of is determined by the Gibbs free energy G as a function of pressure and temperature , in which the contributions from the lattice vibrations and the configurational disorder are obtained within the quasiharmonic and the mean-field approximations, respectively. The stability range of is then illustrated through the phase diagrams. Depending on the temperatures, the stability range of is predicted to be within the range between 40 and 67 GPa. At 500 K, the icosahedral atoms in configurationally disorder at the polar sites. By investigating the properties of , e.g., elastic constants and phonon and electronic density of states, we demonstrate that is both mechanically and dynamically stable at zero pressure, and is an electrical semiconductor. Furthermore, based on the sketched phase diagrams, a possible route for experimental synthesis of as well as a fingerprint for its characterization from the simulations of x-ray powder diffraction pattern are suggested.