Fullerene graphs

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In graph theory, a fullerene graph is a cubic 3-connected planar graph with exactly 12 pentagonal faces and an optional number of hexagonal faces. Fullerene graphs are the Schlegel representations of the corresponding fullerene compounds.

Graph of 20-fullerene w-nodes.svg Graph of 24-fullerene w-nodes.svg Graph of 26-fullerene 5-base w-nodes.svg
20-fullerene (dodecahedral graph) 24-fullerene 26-fullerene
Graph of 60-fullerene w-nodes.svg Graph of 70-fullerene w-nodes.svg
60-fullerene (truncated icosahedral graph) 70-fullerene

(If you only count 11 pentagons, remember that the perimeter counts as one.)