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. 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.
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).
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.
configuration consisting
of 21 points and 21 lines such that four points lie on each line and four lines pass
through each point. 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.
)." J. London Math. Soc. 41, 336-348,
1990.Grünbaum, B.