# Data structures for general (non-tetrahedral) cell complexes

For 2D polygonal meshes, the QuadEdge and HalfEdge data structure representations are sufficient to store and enable efficient query of all topological and incidence information. Are there compact and efficient data structures for 3D polyhedral meshes? I know there has been some recent work on compact representations for tetrahedral meshes, like, for example SOT. I don't know enough about these to know if they generalize to unstructured non-tetrahedral meshes.

I can imagine that half-edges might generalize to half-faces with associated half-edges, but it seems like that is a lot of data to store, and there might be more compact representations. I should add that I really only care about retrieving facet information (like which facets are on the boundary, which facets belong to a certain cell); the edge incidence information is not as useful.

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They are equivalent. In FacetEdge representation, there are mainly 3 functions: clock, Enext and Fnext; and in a 3D combinatorial map, there are 3 functions $\beta_1$, $\beta_2$ and $\beta_3$. –  gdamiand Dec 21 '12 at 8:36