The pentatope graph is the skeleton of the pentatope, namely the complete graph 
. It is sometimes also known as the Kuratowski graph (Nikolić
et al. 2000, p. 281).
Since the 
-simplex
has graph spectrum 
(Cvetkovic et al. 1998, p. 72; Buekenhout
and Parker 1998), the pentatope graph is an integral
graph with graph spectrum 
. The order of its automorphism
group is 
.
The pentatope graph is the line graph of the star
graph 
.
