Editing Abstract polytope (section)

===Flags===

In geometry, a '''[[Flag (geometry)|flag]]''' is a maximal [[Total order#Chains|chain]] of faces, i.e. a (totally) ordered set Ψ of faces, each a subface of the next (if any), and such that Ψ is not a subset of any larger chain. Given any two distinct faces F, G in a flag, either F < G or  F > G.

For example, {'''ø''', '''a''', '''ab''', '''abc'''} is a flag in the triangle '''abc'''.

For a given polytope, all flags contain the same number of faces. Other posets do not, in general, satisfy this requirement.