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## Homework Statement

Zwiebach's A First Course in String Theory

Quick Calculation 2.5: Consider the plane (x,y) with the identification

[tex](x,y)\rightarrow (x+2\pi R,y+2\pi R)[/tex].

What is the resulting space?

## Homework Equations

A one dimensional line with identification [tex]x\rightarrow x+2\pi R[/tex] is a circle.

A plane with identifications

[tex](x,y)\rightarrow (x+2\pi R,y)[/tex]

[tex](x,y)\rightarrow (x,y+2\pi R)[/tex]

is a torus.

## The Attempt at a Solution

The identification is just the combination of both of the torus identifications... but how would I join two boundaries with a single identification? And what would be the fundamental domain? Thanks!