I overlooked the restriction to dimension 3 in you question.
Then indeed the graph would suffice, but there is no shorter representation in polymake than the adjacency matrix (which is given as sets of neighbors for each vertex, so this should be human readable) or a list of all edges.
As the vertex-facet incidence matrix is given in sparse form as a list of vertices per facet this should be close to the densest form you can encode the combinatorial type (up to permutations, which also applies to the graph structures above). In the 3D-case you can get this cyclically ordered with
which prints the vertices of each facet in cyclic order. Again, unique up to relabelling.
Andreas