Editing Abstract polytope (section)

===A simple example===
The faces of the abstract quadrilateral or square are shown in the table below:

{|class=wikitable
|- 
!|Face type 
!Rank (''k'')
!Count
!''k''-faces
|-
|Least ||−1 ||1||''F''<sub>−1</sub> 
|-
|Vertex ||0 ||4||'''a''', '''b''', '''c''', '''d'''
|-
|Edge ||1 ||4||W, X, Y, Z
|-
|Greatest ||2 ||1||G
|}

The relation < comprises a set of pairs, which here include

: ''F''<sub>−1</sub><'''a''', ... , ''F''<sub>−1</sub><X, ... , ''F''<sub>−1</sub><G, ... , '''b'''<Y, ... , '''c'''<G, ... , Z<G.

Order relations are [[Transitive relation|transitive]], i.e. F < G and  G < H implies that F < H. Therefore, to specify the hierarchy of faces, it is not necessary to give every case of F&nbsp;<&nbsp;H, only the pairs where one is the [[Covering relation|successor]] of the other, i.e. where F&nbsp;<&nbsp;H and no G satisfies F&nbsp;<&nbsp;G&nbsp;<&nbsp;H.

The edges W, X, Y and Z are sometimes written as '''ab''', '''ad''', '''bc''', and '''cd''' respectively, but such notation is not always appropriate.

All four edges are structurally similar and the same is true of the vertices. The figure therefore has the symmetries of a square and is usually referred to as the square.