One-point extensions in n_3 configurations

William L. Kocay


Given an n3 configuration, a 1-point extension is a technique that constructs an (n + 1)3 configuration from it. It is proved that all (n + 1)3 configurations can be constructed from an n3 configuration using a 1-point extension, except for the Fano, Pappus, and Desargues configurations, and a family of Fano-type configurations. A 3-point extension is also described. A 3-point extension of the Fano configuration produces the Desargues and anti-Pappian configurations.

The significance of the 1-point extension is that it can frequently be used to construct real and/or rational coordinatizations in the plane of an (n + 1)3 configuration, whenever it is geometric, and the corresponding n3 configuration is also geometric.


Fano configuration, Pappus, Desargues, (n, 3)-configuration

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ISSN: 1855-3974

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