Nanometer-sized carbon cones were generated by vapor condensation of carbon atoms on a graphite substrate and were analyzed by scanning tunneling microscopy (STM), The observed cones are up to 24 nm in length and 8 nm in base diameter. They all have the same cone angle almost-equal-to 19-degrees. This is the smallest among five possible opening angles for perfect graphitic cones. The growth of cones, tubules and C60 may be initiated by fullerene-type nucleation seeds with different number of pentagons.