A pentahedral graph is a polyhedral graph on five nodes. There are two topologically distinct pentahedral graphs which, through
duality, correspond to the skeletons of the square
pyramid (left figure) and triangular dipyramid
(right figure). The pentahedral graphs were first enumerated by Steiner (1828; Duijvestijn
and Federico 1981). The following table gives the convex pentahedra, which have 
, as required by the polyhedral
formula.
| pentahedron | degree sequence |  |  |
| triangular prism | 3, 3, 3, 3, 3, 3 | 6 | 9 |
| square pyramid | 3, 3, 3, 3, 4 | 5 | 8 |
