Starting from a study of the Penrose triangle, the theory is advanced that our perception of the relative spatial positions of parts of a figure is mediated by a set of significant directions (or axes). Illustration and exploration of the theory in this paper revolves around examples drawn mostly from a family of figures related to the Penrose triangle. This family is defined partly in terms of the common nature of its members' anomalies, and partly by the feature that they are seen as configurations of ‘beams’. This feature and the conditions for it are also examined by the use of examples.
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