Editing Abstract polytope (section)

==Formal definition==
An '''abstract polytope''' is a [[partially ordered set]], whose elements we call ''faces'', satisfying the 4 axioms:{{citation needed|date=December 2021|reason=where can this definition be verified?}}

# It has just one [[Abstract polytope#Least and greatest faces|least face]] and one [[Abstract polytope#Least and greatest faces|greatest face]].
# All [[Abstract polytope#Flags|flags]] contain the same number of faces.
# It is [[Abstract polytope#Connectedness|strongly connected]].
# If the ranks of two faces ''a > b'' differ by 2, then there are exactly 2 faces that lie strictly between ''a'' and ''b''.

An '''''n''-polytope''' is a polytope of rank ''n''. The abstract polytope associated with a real [[convex polytope]] is also referred to as its '''[[convex polytope#face lattice|face lattice]]'''.<ref>{{cite journal |first1=Volker |last1=Kaibel |first2=Alexander |last2=Schwartz |url=http://eprintweb.org/S/authors/All/ka/Kaibel/16 |title=On the Complexity of Polytope Isomorphism Problems |journal=[[Graphs and Combinatorics]] |volume=19 |issue=2 |pages=215–230 |year=2003 |arxiv=math/0106093 |doi=10.1007/s00373-002-0503-y |s2cid=179936 |url-status=usurped |archive-url=https://web.archive.org/web/20150721175904/http://eprintweb.org/S/authors/All/ka/Kaibel/16 |archive-date=2015-07-21 }}</ref>