REPETITIVE HIGHER CLUSTER CATEGORIES OF TYPE An

We show that the repetitive higher cluster category of type A(n), defined as the orbit category D-b(mod kA(n))/(tau(-1)[m])(p), is equivalent to a category defined on a subset of diagonals in a regular polygon. This generalizes the construction of Caldero-Chapoton-Schiffler [Quivers with relations arising from clusters (A(n) case), Trans. Amer. Math. Soc. 358(3) (2006) 1347-1364], which we recover when p = m = 1, and the work of Baur-Marsh, [A geometric description of the m-cluster categories, Trans. Amer. Math. Soc. 360(11) (2008) 5789-5803], treating the case p = 1, m > 1. Our approach also leads to a geometric model of the bounded derived category in type A.