19_4 Configuration

A configuration is an abstract configuration of 19 points and 19 lines, with exactly four lines incident with each point and exactly four points incident with each line. Two distinct points are incident with at most one common line. A geometric realization represents these incidences by points and straight lines in the real projective plane, without adding incidences between the selected points and lines.

Abstract configurations exist, and 4028 combinatorial isomorphism classes have topological realizations using pseudolines. However, none has a real geometric realization using straight lines (Bokowski and Pilaud 2015). Thus order 19 is an exception in the existence classification for geometric n₄ configurations.