Geodesic
About Some Mappings Defined by a Classical Desargues Configuration
Journal for geometry and graphics, Tome 17 (2013) no. 1, pp. 69-8.

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A Desargues configuration is a planar figure consisting of ten undistinguished points and ten lines with the well-known meaning of a geometric-algebraic axiom for interpretation as an image of a three-dimensional 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 n-gons, which allow higher dimensional generalizations of the classical interpretation of a Desargues figure in space. Furthermore we consider multi-perspective triangles and an iteration process defined by a pair of not-perspective triangles.
Classification : 51A20, 51A30, 51A05
Mots-clés : Desargues configuration, homology, correlation, polarity, crossratio 
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G. Weiss; F. Manhart . About Some Mappings Defined by a Classical Desargues Configuration. Journal for geometry and graphics, Tome 17 (2013) no. 1, pp. 69-8. http://geodesic.mathdoc.fr/item/JGG_2013_17_1_JGG_2013_17_1_a5/