Editing Abstract polytope (section)

===Faces, ranks and ordering===
In an abstract polytope, each structural element (vertex, edge, cell, etc.) is associated with a corresponding member of the set. The term ''face'' is used to refer to any such element e.g. a vertex (0-face), edge (1-face) or a general ''k''-face, and not just a polygonal 2-face.

The faces are ''ranked'' according to their associated real dimension: vertices have rank 0, edges rank 1 and so on.

Incident faces of different ranks, for example, a vertex F of an edge G, are ordered by the relation  F < G. F is said to be a ''subface'' of G.

F, G are said to be ''incident'' if either F = G or F < G or G < F. This usage of "incidence" also occurs in [[finite geometry]], although it differs from traditional geometry and some other areas of mathematics. For example, in the square ''ABCD'', edges ''AB'' and ''BC'' are not abstractly incident (although they are both incident with vertex B).{{citation needed|date=December 2016|reason=equals sign undefined. F ranked equally to G is not sufficient condition for geometrical incidence, on the other hand F equating to G would mean they are the same face.}}

A polytope is then defined as a set of faces '''P''' with an order relation '''<'''. Formally, '''P''' (with '''<''') will be a (strict) [[partially ordered set]], or ''poset''.