Fullerene graphs
cubic planar graph with all faces of size 5 or 6
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.
|
|
|
| 20-fullerene (dodecahedral graph) | 24-fullerene | 26-fullerene |
|
| |
| 60-fullerene (truncated icosahedral graph) | 70-fullerene |
(If you only count 11 pentagons, remember that the perimeter counts as one.)