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 .