It can be expressed as the product of two circles, but like the Klein bottle is more often viewed as a square with opposite sides identified.  
This two dimensional manifold is orientable and has Euler characteristic 0.  It can be expressed as the product of two circles, but like the Klein bottle is more often viewed as a square with opposite sides identified.  FTP, name this surface, which is more familiar to most people as the surface of a donut.
This two dimensional manifold is orientable and has Euler characteristic 0.  
Torus