Data structures for general (non-tetrahedral) cell complexes
There is an extension of half-edge in any dimension, called darts in combinatorial maps.
There are two packages in CGAL allowing to use these combinatorial maps in any dimension (see here for combinatorialMaps and here for LinearCellComplex).

You can use this data structure to represent any Quasi manifold orientable subdivided 3D object. Quoting from CGAL webpage(section 2.4 Combinatorial Map Properties):

A quasi-manifold object is defined as:


  A dD quasi-manifold is an object obtained by taking some isolated d-cells, and allowing to glue d-cells along (d-1)-cells.


and orientable as:


  It is orientable if it is possible to embed it in the Euclidean space and to define a global "left" and "right" direction in each point of the embedded object.