Surfaces (Geometry and the Imagination)
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Conway, Doyle, Gilman, Thurston; The Geometry Center  
A surface, or 2manifold, is a shape any small enough neighborhood of which is topologically equivalent to a neighborhood of a point in the plane. For instance, a the surface of a cube is a surface topologically equivalent to the surface of a sphere. Some pictures of surfaces are provided. The pictures are intended to indicate things like doughnuts and pretzels rather than flat strips of paper. Can you identify these surfaces topologically? Which ones are topologically the same intrinsically, and which extrinsically?  


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