Carboncones, a special family of all-carbon allotropes, are predicted to have unique properties that distinguish them from fullerenes, carbon nanotubes, and graphenes. Owing to the absence of methods to synthesize atomically well-defined carboncones, however, experimental insight into the nature of pure carboncones has been inaccessible. Herein, we describe a facile synthesis of an atomically well-defined carboncone[1,2] (C70H20) and its soluble penta-mesityl derivative. Identified by x-ray crystallography, the carbon skeleton is a carboncone with the largest possible apex angle. Much of the structural strain is overcome in the final step of converting the bowl-shaped precursor into the rigid carboncone under mild reaction conditions. This work provides a research opportunity for investigations of atomically precise single-layered carboncones having even higher cone walls and/or smaller apex angles.