The Grünbaum-Rigby configuration is a configuration consisting
of 21 points and 21 lines such that four points lie on each line and four lines pass
through each point (left figure above). It was first described by Klein (1879), but
a geometric realization in the Euclidean plane
was not found until Grünbaum and Rigby (1990) constructed one by overlaying
three regular heptagrams. Note that the points also
determine seven additional lines through three ponts (illustrated in red in the right
figure above) which are not however part of the configuration.

The best known solution to the orchard-planting problem for 22 points with 4 points per line is obtained by a adding a point
at the center of the configuration through which opposite vertices of the configuration
lie, yielding 28 lines (E. Pegg, Jr., pers. comm., Dec. 11, 2023). Note
that this arrangement is not a configuration since
while five lines pass through 21 of the points, seven lines pass through the central
point.

Burnside, W. "On the Hessian Configuration and Its Connection With the Group of 360 Plane Collineations." Proc. London Math.
Soc.4, 54-71, 1907.Coxeter, H. S. M. "My
Graph." Proc. London Math. Soc.46, 117-136, 1983.Grünbaum,
B. and Rigby, J. F. "the Real Configuration ()." J. London Math. Soc.41, 336-348,
1990.Grünbaum, B. Configurations
of Points and Lines. Providence, RI: Amer. Math. Soc., p. 311, 2009.Klein,
F. "Über die Transformation siebenter Ordnung der elliptischen Functionen."
Math. Ann.14, 428-471, 1879.