Abstract In this paper, we discuss some topics related to external representation in geometry and their implications on its learning. First, we analyse the different natures of geometrical and representative spaces (in the sense of Poincare) and the question of the double status of geometrical objects; then, we focus on the typicality of geometrical representations. The last question considered here concerns the role and the nature of an external representation in geometry. The analysis is made on an epistemological basis, taking into account some empirical research results.