A simple way to tell a simple polytope from its graph
Let P be a simple d-dimensional polytope and G(P) be the graph of P. Two vertices u and v in V(P) are adjacent in G(P) if [v,u] is a 1-dimensional face of P. Recently, \textit{R. Blind} and \textit{P. Mani-Levitska} [Aequationes Math. 34, 287-297 (1987; Zbl 0634.52005)] proved a conjecture of Perles that G(P) determines the entire combinatorial structure of P. In this note the author gives a simple proof of this result.
scientific article; zbMATH DE number 4101271