A 
configuration is an abstract configuration of 23
points and 23 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.
Lu (2026) constructed real geometric examples, settling the last unresolved order for geometric n4 configurations.
One example has homogeneous coordinates 
, 
, 
, 
, 
, 
, 
, and 
for its points. Its
lines are 
, 
, 
, 
, 
, 
, 
, and 
, where all sign combinations are taken independently
(Lu 2026).
Lu (2026) also constructed an example defined over 
but not over 
. The two examples are the only ones with a Vierergruppe
of projective symmetries, up to projective equivalence. They are not the only geometric
configurations.
Configurations and the End of the Existence Problem for
Geometric 
Configurations." 8 Oct 2026.