Flag

A flag is a set of a polytope's elements that contains exactly one element of each rank, such that any two elements in it are incident. More formally, a flag is a maximal chain in the element lattice.

Flags are useful for computing certain properties or carrying out certain constructions of highly symmetric polytopes.

Flag Changes
One useful operation on flags are n-flag changes. These replace exactly one element of a certain rank in the flag with another adjacent one, where n denotes the rank of the element you're changing. Because of the requirement of dyadicity, an n-flag change has only one outcome. Another consequence of this is that any flag change applied twice will result in the starting flag.