The House in Four Dimensions is a Theorem

This paper deals with the construction of a possible architectural project in four dimensions. It is part of a research on the design theory and related analysis of the compositional process, and on the changing of paradigms in Architecture. To demonstrate the hypothesis of the real consistency of a new 4d spatiality for the Architecture, the design process has been analyzed in form of a theorem, starting from the comparison between the elements of the project and the definitions of the referred geometry, acquired from the study of the mathematical treatises on the fourth dimension. The adopted method is: following the scientific process, proceeding from the exposition of the problem, acquisition of the state of the art, description of the steps of the research, formulation of the hypothesis and demonstration of the theoretical assumption.