The order complex of a partially ordered set 
is the abstract
simplicial complex whose 0-dimensional simplices
are elements of 
and whose simplices are its finite
nonempty chains. A chain 
therefore gives a 
-dimensional simplex. This construction
turns partial order relations into topological data.
For two incomparable elements, the complex is two isolated points. For a two-element chain it is an interval. The subgroup order complex in the Quillen conjecture uses inclusion of elementary Abelian subgroups as its partial order relation.
