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A pentahedron is a polyhedron having five faces. Through duality, the two polyhedral 5-vertex graphs correspond to the two convex pentahedra with the topologies of the square pyramid and the triangular prism.
 |  |  | name |
| 5 | 5 | 8 | square pyramid |
| 5 | 6 | 9 | triangular prism |
For these pentahedra, 
,
as required by the polyhedral formula. The
degree sequence of the skeleton
of the square pyramid is (3, 3, 3, 3, 4), and that
of the triangular prism is (3, 3, 3, 3, 3, 3).
The convex pentahedra are illustrated above, together with their skeletons and the corresponding polyhedral 5-vertex graphs (the dual graphs of their skeletons).
