A pentahedral graph is a polyhedral graph on five vertices. 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 |
