A 
configuration is an abstract configuration of 21
points and 21 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.
The Grünbaum-Rigby configuration and the Berman-Gévay-Pisanski
configuration are nonisomorphic real geometric examples. Berman et al. (2024)
classified the polycyclic configurations
of this order: there are 17 abstract polycyclic
configurations up to isomorphism, exactly two
of which have geometric polycyclic realizations. These two are the named examples
above. The polycyclic classification does not classify all 
configurations.
)
Polycyclic Configuration." Elec. J. Combin. 31, P4.54, 2024.