The intergrowth crystal of n-tetracosane/urea presents a misfit parameter, defined by the ratio γ=ch/cg(chost/cguest), that is very close to a commensurate value (γ≅1/3). High-resolution diffraction studies presented here reveal an aperiodic misfit parameter of γ=0.3369, which is found to be constant at all temperatures studied. A complex sequence of structural phases is reported. The high temperature phase (phase I) exists in the four-dimensional superspace group P6122(00γ). At Tc1=179(1)K, a ferroelastic phase transition increases the dimension of the crystallographic superspace. This orthorhombic phase (phase II) is characterized by the five-dimensional (5D) superspace group C2221(00γ)(10δ) with a modulation vector ao∗+cm∗=ao∗+δ·ch∗, in which the supplementary misfit parameter is δ=0.025(1) in host reciprocal units. This corresponds to the appearance of a modulation of very long period (about 440±16Å). At Tc2=163.0(5)K, a 5D to 5D phase transition leads to the crystallographic superspace group P212121(00γ)(00δ) with a very similar value of δ. This phase transition reveals a significant hysteresis effect.