Molecular surfaces are one of the most widely used visual representations for the analysis of molecules. They allow different properties of the molecule to be shown and allow additional information to be added, such as chemical properties of the atoms, using colour. With the usual representation of molecular surfaces being three dimensional there are common problems, such as occlusion and view-dependency. To solve these problems a two dimensional representation of the molecular surface can be created. For molecules with a surface of genus zero there are different methods of creating the sphere that is used as an intermediate object to create the map. For molecules with a higher genus this process becomes more difficult. Tunnels can only be mapped to the sphere if they are closed at some point inside the tunnel. Introducing arbitrary cuts can lead to small areas on the map. The deeper inside the tunnel the cut is placed the smaller the area. To avoid these small areas the cuts have to be placed close to the entrance of the tunnel. Therefore a mesh segmentation is performed to identify the tunnel and to create a genus zero surface for the molecule. Based on this identification further information can be displayed, such as geodesic lines showing how the tunnels are connected.