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A seminal result of E. Ehrhart states that the number of integer latticepoints in the dilation of a rational polytope by a positive integer $k$ is aquasi-polynomial function of $k$ --- that is, a "polynomial" in which thecoefficients are themselves periodic functions of $k$. Using a result of F. Liuon the Ehrhart polynomials of cyclic polytopes, we constructnot-necessarily-convex rational polytopes of arbitrary dimension in which theperiods of the coefficient functions appearing in the Ehrhart quasi-polynomialtake on arbitrary values.

Rational polytopes with Ehrhart coefficients of arbitrary period