The article is an attempt to show how certain basic geometrical concepts, e.g. 'straight', 'circle', 'sphere', 'square', 'cube' and 'triangle', are used in cognition and language. A number of psychological arguments are adduced, based mainly on the findings of Gestalt psychologists, showing that they are indeed cognitively salient. It is argued that there seems to be a set of basic geometrical figures and shapes in terms of which space is conceptualized (which is just a slight reformulation of the fundamental insight of the Cubists). These figures and shapes seem to have all the major characteristics of basic-level categories as discussed by Rosch and her associates. As cognitively salient concepts, they provide rich sources for metaphoric extensions, either in terms of their "literal", geometrical forms or in terms of their typical instantiations. An attempt is made to establish the direction of the diachronic development of senses of the predicates designating the basic figures and shapes in Polish and English, i.e. from geometrical to concrete or from concrete to geometrical, and to explain the possible reasons for the direction of those sense extensions. The paper ends with a brief discussion of the question whether or not the basic geometrical shapes may also function as preconceptual image schemas. (Boguslaw Bierwiaczonek)