The Desargues configuration

If you draw the green and blue parts of a Desargues configuration like the one on the left in any classical projective plane or space, then the three orange points are always contained in a line. This property characterizes these classical geometries. 

As an abstract geometry the Desargues configuration is one of the 10 linear 10_3 configurations.


This is a spatial model of the (abstract) Desargues configuration.