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In this paper, we want to document the history of the models of mathematical surfaces used for the didactics of pure and applied “High Mathematics”, in Italy and in Europe. These models were built between the second half of nineteenth century and the 1930s. We want here also to underline several important links that put in correspondence conception and construction of models with scholars, cultural institutes, specific views of research and didactical studies in mathematical sciences and with the world of the figurative arts furthermore, by using short descriptions and opportune examples.