One-point extensions in nsub3 configurations - Kocay, William Lawrence (Ars mathematica contemporanea, 2016)
Given an ?$n_3$? 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 ?$n_3$? 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 ?$n_3$? configuration is also geometric.
Keywords: geometrija; konfiguracije