The band structure of rhombohedral graphite has been investigated using the nearest-neighbor tight-binding approximation. The resulting behavior of the π-bands near the Fermi surface is more complex than in the case of the Bernal stacking. The two π-bands still touch, but the touching points no longer lie on the edges of a hexagonal prism in k-space. Instead, they lie on cylinders whose axes are the edges of the hexagonal prism. The radii of these cylinders are proportional to γ1, the nearest "out-of-plane" exchange integral. The de Haas – Van Alphen effect in the rhombohedral structure may be expected to yield useful information about the magnitude of γ1.