The face lattice of the surface organized as a directed graph.
Each node corresponds to some proper face of the surface.
The nodes corresponding to the vertices and facets appear in the same order
as the elements of GEOMETRIC_REALIZATION and FACETS properties.
Two special nodes represent the whole surface and the empty face.
Reordered DUAL_GRAPH for surfaces.
The neighbor facets are listed in the order corresponding to FACETS_CYCLIC,
so that the first two vertices in FACETS_CYCLIC make up the ridge to the first neighbor
facet and so on.
A Morse matching is a reorientation of the arcs in the Hasse diagram of a simplicial complex
such that at most one arc incident to each face is reoriented (matching condition) and the
resulting orientation is acyclic (acyclicity condition). Morse matchings capture the main
structure of discrete Morse functions, see
Robin Forman: Morse Theory for Cell-Complexes,
Advances in Math., 134 (1998), pp. 90-145.
This property is computed by one of two heuristics. The default heuristic is
a simple greedy algorithm (greedy). The alternative is to use a canceling algorithm
due to Forman (cancel). Note that the computation of a Morse matching of largest
size is NP-hard. See
Michael Joswig, Marc E. Pfetsch: Computing Optimal Morse Matchings