Hans Reichenbach's so-called geometrical conventionalism is often taken as an example of a positivistic philosophy of science, based on a verificationist theory of meaning. By contrast, we shall argue that this view rests on a misinterpretation of Reichenbach's major work in this area, the Philosophy of Space and Time (1928). The conception of equivalent descriptions, which lies at the heart of Reichenbach's conventionalism, should be seen as an attempt to refute Poincaré's geometrical relativism. Based upon an examination of the reasons (...) Reichenbach gives for the cognitive equivalence of geometrical descriptions, the paper argues that his conventionalism is a specific form of scientific realism. At the same time we shall argue against those interpretations which lead to a trivialization of Reichenbach's conventionalism or deny it entirely. (shrink)