The church of St Ignatius of Loyola in Rome, together with the Church of the Gesù, represents the most significant artistic contribution of the Jesuits in the Eternal City. Incorporated in the broader context of the Roman College, and built between 1626 and 1650 following a project by Padre (Father) Orazio Grassi S.J., it is the only one of the great Roman churches without a dome. The projects for the helioscopic dome by Orazio Grassi, the Cortonesque dome by Armando Brasini and the perspective dome by Andrea Pozzo represent the difficult attempt to create a perfectly rational layout for Rome, an ideal scientific and theological city. These projects tell the story of three different ways of conceiving architectural space affecting the city: political manifesto, imaginative introspection and colossal scenography. This paper describes the history of an “impossible” dome, analysing the historical evolution of the project and its three potential authors, three magnificent and idealist designers.