O = orderComplex P
The order complex of a poset is the SimplicialComplex with vertices corresponding to the ground set of $P$ and faces corresponding to the chains of $P$.

The minimal nonfaces are given by the incomparable pairs of vertices in $P$. Thus the order complex is the independence complex of the incomparabilityGraph of $P$ and the clique complex of the comparabilityGraph of $P$. Moreover, the facets are given by the maximalChains of $P$. Thus, the order complex of a chain poset is a simplex.

This method renames the vertices with integers $0, 1, \ldots$ corresponding to the index of the vertices in the GroundSet.
The object orderComplex is a method function with options.