
Journal for Geometry and Graphics 17 (2013), No. 1, 069080 Copyright Heldermann Verlag 2013 About Some Mappings Defined by a Classical Desargues Configuration Gunter Weiss Inst. of Discrete Mathematics and Geometry, University of Technology, Wiedner Hauptstr. 810/104, 1040 Vienna, Austria Friedrich Manhart Inst. of Discrete Mathematics and Geometry, University of Technology, Wiedner Hauptstr. 810/104, 1040 Vienna, Austria manhart@dmg.tuwien.ac.at A Desargues configuration is a planar figure consisting of ten undistinguished points and ten lines with the wellknown meaning of a geometricalgebraic axiom for interpretation as an image of a threedimensional figure. We consider the ten homologies defined by such a configuration. We give an analytic proof for the fact that such a configuration defines a unique polarity too. The (labelled) Desargues figure, i.e., two perspective triangles together with the perspectivity center and axis, can be extended to perspective ngons, which allow higher dimensional generalizations of the classical interpretation of a Desargues figure in space. Furthermore we consider multiperspective triangles and an iteration process defined by a pair of notperspective triangles. Keywords: Desargues configuration, homology, correlation, polarity, crossratio. MSC: 51A20; 51A30, 51A05 [ Fulltextpdf (643 KB)] for subscribers only. 