In the mathematical field of graph theory, the 26-fullerene graph is a polyhedral graph with V = 26 vertices and E = 39 edges. Its planar embedding has three hexagonal faces (including the one shown as the external face of the illustration) and twelve pentagonal faces. As a planar graph with only pentagonal and hexagonal faces, meeting in three faces per vertex, this graph is a fullerene. The existence of this fullerene has been known since at least 1968.
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