Creating a PolyhedronData[] structure for custom polyhedra

The PolyhedronData[] structure is wonderfully rich. I would like to create data for my own polyhedra, not any of the many that Mathematica provides. Is this possible? I wouldn't need every property, but I would like it to function the same way, e.g., PolyhedronData["MyPolyhedron", "VertexCoordinates"] would return a list of vertex coordinates, etc. I can hack up MyPolyhedronData[], but I would prefer to use PolyhedronData[] if possible. Thanks for ideas!

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Something like what was done here could be applicable to this case, I suppose. – J. M. Sep 28 '12 at 18:39