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To classify conformally inequivalent tori, one introduces the parameter tau. Tori with tau =tau +1 and tau = -1/tau are conformally equivalent.

Now, consider two conformally inequivalent tori. Let's say one has tau =i and the other one has tau = i +1/2.

Zwiebach calls the first one a "rectangular torus".

How can we visualize the torus with tau = i+1/2 ?

Zwiebach draws a picture in figure 23.18 but I don't get it.The figure indicates that if we move along one cycle of a torus, we end up shifted a certain amount in the perpendicular direction. I don't understand how we can not, for

*any*torus, simply go along a cycle and get back to the same position. That seems trivially possible for any torus!

Hope someone can clarify this.

Thanks