We call 3n the class of 3-valent plane graphs whose faces are 3-gons (necesarily four 3-gons) or 6-gons.
The classification of possible point groups was obtained in
P.W. Fowler, J.E. Cremona and J.I. Steer, "Systematics of bonding in non-icosahedral carbon clusters", Theor. Chim. Acta 73 (1988) 1--26.