Flag graph

A flag graph is a way to express the structure of a polytopes flags.

The flag graph of an abstract polytope is a maniplex, although not all mainplexes are the flag graph of a polytope.

Definition
Two flags of a polytope are $j$-adjacent if they differ in exactly one element of rank $j$.

The flag graph is a edge colored graph with vertices corresponding to the flags of a polytope and with $i$ colored edges between flags that are $i$-adjacent.