Geodesic
Extended affine Weyl groups of type $A_1$.
Journal of Algebraic Combinatorics, Tome 28 (2008) no. 4, pp. 481-493.

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Summary: It is known that elliptic Weyl groups, extended affine Weyl groups of nullity 2, have a finite presentation called the generalized Coexter presentation. Similar to the finite and affine case this presentation is obtained by assigning a Dynkin diagram to the root system. Then there is a prescription to read the generators and relations from the diagram. Recently a similar presentation is given for simply laced extended affine Weyl groups of nullity 3 and rank>1. Employing a new method, we complete this work by giving a similar presentation for nullity 3 extended affine Weyl groups of type $A _{1}$.
Keywords: keywords Dynkin diagram, Weyl groups, root system 
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     author = {Azam, Saeid and Shahsanaei, Valiollah},
     title = {Extended affine {Weyl} groups of type $A_1$.},
     journal = {Journal of Algebraic Combinatorics},
     pages = {481--493},
     publisher = {mathdoc},
     volume = {28},
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     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2008__28_4_a3/}
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Azam, Saeid; Shahsanaei, Valiollah. Extended affine Weyl groups of type $A_1$.. Journal of Algebraic Combinatorics, Tome 28 (2008) no. 4, pp. 481-493. http://geodesic.mathdoc.fr/item/JAC_2008__28_4_a3/