The human islet amyloid polypeptide (hIAPP) is the primary component in the toxic islet amyloid deposits in type-2 diabetes. hIAPP self-assembles to aggregates that permeabilize membranes and constitutes amyloid plaques. Uncovering the mechanisms of amyloid self-assembly is the key to understanding amyloid toxicity and treatment. Although structurally similar, hIAPP's rat counterpart, the rat islet amyloid polypeptide (rIAPP), is non-toxic. It has been a puzzle why these peptides behave so differently. We combined multiscale modelling and theory to explain the drastically different dynamics of hIAPP and rIAPP: The differences stem from electrostatic dipolar interactions. hIAPP forms pentameric aggregates with the hydrophobic residues facing the membrane core and stabilizing water-conducting pores. We give predictions for pore sizes, the number of hIAPP peptides, and aggregate morphology. We show the importance of curvature-induced stress at the early stages of hIAPP assembly and the α-helical structures over β-sheets. This agrees with recent fluorescence spectroscopy experiments.