  We consider the unconstrained traveling tournament problem, a sports
timetabling problem that minimizes traveling of teams. Since its introduction
about 20 years ago, most research was devoted to modeling and reformulation
approaches. In this paper we carry out a polyhedral study for the cubic integer
programming formulation by establishing the dimension of the integer hull as
well as of faces induced by model inequalities. Moreover, we introduce a new
class of inequalities and show that they are facet-defining. Finally, we
evaluate the impact of these inequalities on the linear programming bounds.
