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A model for the PlanarMapDcel_2 concept defines the underlying combinatorial data structure (halfedge data structure) used in the planar map data structure Planar_map_2<Dcel,Traits>.
The PlanarMapDcel_2 concept is a refinement of the TopologicalMapDcel. Hence, the requirements for the latter are requirements for the former. The difference in requirements is that the Vertex and Halfedge types should be models of the more refined concepts PlanarMapDcelVertex_2 and PlanarMapDcelHalfedge_2.
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The vertex type. Should be a model of the
PlanarMapDcelVertex_2 concept.
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The halfedge type. Should be a model of the
PlanarMapDcelHalfedge_2 concept.
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The concept ArrangementDcel_2 is not (!) a refinement of PlanarMapDcel_2. Using a model of the ArrangementDcel_2 such as CGAL::Arr_2_default_dcel<Traits> will result in an error.