How to store face properties for a CGAL Nef_Polyhedra for convex decomposition

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I need to use the CGAL convex decomposition algorithm but it seems to only work for a Nef_Polyhedra object. Also, my 3D mesh needs to have face properties (like those provided by the Surface_mesh object, see example). And I'd like to keep the face properties while performing the convex decomposition.

The face properties are defining a texture UV mapping, each face can have a different texture.

Is there a way to assign properties to faces for the Nef_polyhedra objects, and more important, have a way to keep those properties while the object is being transformed. On Surface_mesh the mesh processing corefine algorithms can use a visitor to define the properties on the transformed mesh based on the source mesh properties. Is there a similar pattern available for Nef_Polyhedra?

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