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We consider the unconstrained traveling tournament problem, a sportstimetabling problem that minimizes traveling of teams. Since its introductionabout 20 years ago, most research was devoted to modeling and reformulationapproaches. In this paper we carry out a polyhedral study for the cubic integerprogramming formulation by establishing the dimension of the integer hull aswell as of faces induced by model inequalities. Moreover, we introduce a newclass of inequalities and show that they are facet-defining. Finally, weevaluate the impact of these inequalities on the linear programming bounds.

A Polyhedral Study for the Cubic Formulation of the Unconstrained Traveling Tournament Problem