Lower Fullerenes

Lower fullerenes are fullerene molecules consisting of fewer than 60 carbon atoms. They are cage-like fused-ring structures made of hexagons and pentagons, with a carbon atom at the vertices of each polygon and a bond along each polygon edge.

Any fullerene with hexagons, pentagons and no other polygons must exactly have 12 pentagons. These fullerenes obey the rule a = 2(n + 10), where n is the number of hexagons and a is the number of carbon atoms.^[1]

• Errera graph, the dual graph of one of the C30 fullerenes

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