Françoise Choay, during the preparation of her book L’Urbanisme, Utopies et Réalités (Urbanism, Utopias and Realities), asked Xenakis (who at the time was living in Berlin as a Ford Foundation grant holder) to make a proposal for the city of the future. The composer-architect was impregnated with the urbanistic discourses of the sixties, which magnified technology and questioned the sprawl of cities, the latter constituting one of the theoretical pillars of the modern movement of the beginning of the century. He makes his proposal a true utopia. Xenakis proposes several towers in the form of hyperboloids of revolution, stretching up to 5 km in height, not without recalling that of the Assembly of Chandigarh. This set of towers shelters a city of 500 0000 inhabitants, thanks to a system of ventilation and circulation. To live on the Earth vertically, to touch the clouds and to open up to galactic space, these dreams of Xenakis will reappear later in the Polytopes.