Hi, everyone:

   I have been going over some simplicial homology recently, hoping to get  
   some geometric insight that I don't know how to get from the algebraic
   machinery alone.

   I have been trying to find the homology of the torus this way, i.e., by
   triangulating it ( i.e., finding a carrier for the torus), but the smallest
   triangulation I have been able to do , has 18 triangles/faces --I checked it works;
   there are 8 vertices and 26 edges.
     Still: does anyone know of a simpler triangulation, ie., one with a smaller total
  number of triangles (and, of course, fewer vertices and edges resp.). ?

   I had tried the long shot of solving the very simple equation:

   V-E+F =0  


  in positive integers.
   
 but this alone does not seem to help . Any ideas.?. Any ideas for
   finding minimal triangulations of surfaces, or higher-dimensional manifolds.?

   Thanks.