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).
The pentatope graph is implemented in the Wolfram Language as GraphData["PentatopeGraph"].
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 group order of
its automorphism group is 
. The pentatope graph is the line
graph of the star graph 
.
The pentatope graph is an outer-cylindrical forbidden minor No. 2 (Archdeacon et al. 2001).
."