A polyhedral 5-vertex graph is a polyhedral graph on five vertices. There are two nonisomorphic polyhedral 5-vertex graphs illustrated above as the skeletons of the square pyramid (left figure) and triangular dipyramid (right figure). Through duality, these graphs correspond to the five-faced polyhedra enumerated by Steiner (1828), as documented by Duijvestijn and Federico (1981).
The name "pentahedral graph" is also used for this class (Gayathri 2018, p. 50).
