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We construct a noncommuting quadrilateral of factors whose upper sides areeach the Asaeda-Haagerup subfactor with index $\frac{5+\sqrt{17}}{2} $ byshowing the existence of a Q-system in the Asaeda-Haagerup category with index$\frac{7+\sqrt{17}}{2} $.

A quadrilateral in the Asaeda-Haagerup category