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In (polyhedral) geometry, a flag is a sequence of faces of a polytope, each contained in the next, with just one face from each dimension. More formally, a flag ψ of an ''n''-polytope is a set such that ''F''''i'' ≤ ''F''''i''+1 (−1 ≤ ''i'' ≤ ''n'' − 1) and there is precisely one ''F''''i'' in ''ψ'' for each ''i'', (−1 ≤ ''i'' ≤ ''n''). Since, however, the minimal face ''F''−1 and the maximal face ''F''''n'' must be in every flag, they are often omitted from the list of faces, as a shorthand. These latter two are called improper faces. For example, a flag of a polyhedron comprises one vertex, one edge incident to that vertex, and one polygonal face incident to both, plus the two improper faces. A flag of a polyhedron is sometimes called a "dart". A polytope may be regarded as regular if, and only if, its symmetry group is transitive on its flags. This definition excludes chiral polytopes. ==Incidence geometry== In the more abstract setting of incidence geometry, which is a set having a symmetric and reflexive relation called ''incidence'' defined on its elements, a flag is a set of elements that are mutually incident. This level of abstraction generalizes both the polyhedral concept given above as well as the related flag concept from linear algebra. A flag is ''maximal'' if it is not contained in a larger flag. When all maximal flags of an incidence geometry have the same size, this common value is the ''rank'' of the geometry. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Flag (geometry)」の詳細全文を読む スポンサード リンク
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