I'm watching a naive introduction to the Möbius band, the lecturer asks if it's possible to construct a one sided surface and then she says that there is one of these surfaces, namely the Möbius band. Then she mentions that some surfaces have two sides.

I've also had this doubt when reading Flegg's *From Geometry to Topology*. So, is it possible to have a surface with more than two sides? My intuition says no, but perhaps someone made some magic trick and made it somehow. I've looked at some wikipedia articles and I've seen no mention to something with more than two surfaces (I've used my browser search tool), unless such surfaces have other names.

I guess that the tags should be *geometry* and *topology*, if you think there is something more, please edit.