In fact, the conformal type of the torus is determined by the cross-ratio of the four points. n-dimensional torus
The torus has a generalization to higher dimensions, the n-dimensional torus, often called the n-torus or hypertorus for short. (This is the more typical meaning of the term "n-torus", the other referring to n holes or of genus n.) Recalling that the torus is the product space of two circles, the n-dimensional torus is the product of n circles.
The fundamental group of the torus is just the direct product of the fundamental group of the circle with itself:

  
    
      
        
          π
          
            1
          
        
        (
        
          
            T
          
          
            2
          
        
        )
        =
        
          π
          
            1
          
        
        (
        
          S
          
            1
          
        
        )
        ×
        
          π
          
            1
          
        
        (
        
          S
          
            1
          
        
        )
        ≅
        
          Z
        
        ×
        
          Z
        
        .