The energy band structure, equation of state, d. of states, and elastic moduli of a new allotropic carbon modification, namely, fullerite C24 with a simple cubic lattice (known previously as cubic graphite), are calcd. by the full-potential linearized APW (FLAPW) method with geometry optimization for the first time. The dependence of the total energy on the lattice const. exhibits a min. for a0 = 0.60546 nm. In this case, the lengths of the C-C bonds between fullerene mols., the lengths of the 6,6-bonds shared by hexagons, and the lengths of the 4,6-bonds shared by a square and a hexagon are equal to 0.1614, 0.1503, and 0.1637 nm, resp. An anal. of the energy band structure and the d. of states demonstrates that the simple cubic fullerite C24 is a direct-band-gap insulator or a semiconductor with a band gap of 1.6 eV. The calcd. bulk modulus B 0 = 196 GPa and the elastic moduli C11 = 338 GPa, C12 = 139 GPa, and C44 = 30 GPa indicate that the fullerite under investigation is a mech. stable material. The inference is made that the simple cubic fullerite C24 is a new diamond-like mol. zeolite with a unique combination of properties, such as the porosity and nonpolarizability, on the one hand, and the mech. strength, chem. inertness, and high thermal cond., on the other hand. The simple cubic fullerite C24 can be considered a promising low-dielec.-const. (low-k) material (Îµ0 < 5.7) for use in fabricating interconnections and substrates intended for integrated circuits and nanoelectronics.