A simplicial complex is represented as a list of its inclusion maximal faces, encoded as ordered sets of their vertices. The topaz standard requires the list of facets to be free of redundancies and the vertices to be numbered consecutively starting with 0. The empty complex is represented as a single empty set.
Therefore nearly all topaz clients expect a non-empty property FACETS containing inclusion maximal sets of integers ranging from 0 to n-1.
If you are not sure whether the initial description of your complex conforms to the topaz standard, you should store it in the data file as INPUT_FACES. Then topaz will automatically remove all redundancies.
Since the vertex numbering is restricted, you are welcome to define VERTEX_LABELS. This section is an array, containing a string of characters (letters, digits, underscore, punctuation characters, etc. but no blanks) for each vertex. You may choose any distinct name for each vertex. As the default topaz uses the vertex numbering as labels.
Any operation identifying vertices (e.g. the non-disjoint union of two complexes) relies on these labels. The labels also help you to keep track of special vertices throughout a series of constructions. Clients producing new complexes keep the old labels whenever appropriate, or construct the new labels from the old ones basing on a well-defined scheme.
The automatic conversion from INPUT_FACES into FACETS mentioned above takes care of vertex numbering too. If the input vertices are not numbered consequently, they are renumbered and the original vertex numbers become VERTEX_LABELS.
All clients constructing a new simplicial complexes from scratch produce a new file containing a FACETS section according to the topaz standard. If a client constructs a new simplicial complex from others, it still produces a new file containing a FACETS section, yet it labels the vertices depending on the original labeling.
Most of the topaz clients consider a subcomplex as a complex in its own right and therefore produce a new file containing a FACETS and a VERTEX_LABELS section (e.g. k_skeleton). However sometimes a subcomplex is viewed as a property of the original complex (e.g. boundary_of_pseudo_manifold). In this case, the client produces a new section within the original file and does not adjust the numbering. Therefore the vertices of the subcomplex have the same numbering as in FACETS, rather than being renumbered from 0 to n-1.
If you would like to view the subcomplex as a separate complex, use the extract_subcomplex client.