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In page Pancyclic graph:
"A maximal planar graph is a planar graph in which all faces, even the outer face, are triangles. A maximal planar graph is node-pancyclic if and only if it has a Hamiltonian cycle:[2] if it is not Hamiltonian, it is certainly not pancyclic, and if it is Hamiltonian, then the interior of the Hamiltonian cycle forms a maximal outerplanar graph on the same nodes, to which the previous argument for maximal outerplanar graphs can be applied.[3] For instance, the illustration shows the pancyclicity of the graph of an octahedron, a Hamiltonian maximal planar graph with six vertices. More strongly, by the same argument, if a maximal planar graph has a cycle of length k, it has cycles of all smaller lengths.[4]
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