
REFERENCES

A. Betten and D. Betten, Regular linear spaces, Beitraege zur Algebra und Geometrie, 38 (1997), 111124.
A. Betten and D. Betten, Tactical decompositions and some configurations v_4, J. Geom. 66 (1999), 2741.
A. Betten, G. Brinkmann and T. Pisanski, Counting symmetric configurations v_3, Discrete Appl. Math., 99 (2000), 331338.
M. Boben et al., Small trianglefree configurations of points and lines, Discrete Comput. Geom., 35 (2006), 405427.
Bokowski and Sturmfels, Comput. Synthetic Geom., Lect Notes Math. 1355, p. 41.
CRC Handbook of Combinatorial Designs, 1996, p. 255.
H. Gropp, Configurations and their realization, Discr. Math. 174 (1997), 137151.
Branko Grünbaum, Configurations of Points and Lines, Graduate Studies in Mathematics, 103 (2009), American Mathematical Society.
D. Hilbert and S. CohnVossen, Geometry and the Imagination Chelsea, NY, 1952, Ch. 3.
F. Levi, Geometrische Konfigurationen, Hirzel, Leipzig, 1929.
Pisanski, T.; Boben, M.; Marusic, D.; Orbanic, A.; and Graovac, A. The 10cages and derived configurations. Discrete Math. 275 (2004), 265276.
Pisanski, T. and Randic, M., Bridges between Geometry and Graph Theory, in Geometry at Work: Papers in Applied Geometry (Ed. C. A. Gorini), M.A.A., Washington, DC, pp. 174194, 2000.
B. Polster, A Geometrical Picture Book, Springer, 1998, p. 28.
Sturmfels and White, Rational realizations..., in H. Crapo et al. editors, Symbolic Computation in Geometry, IMA preprint, Univ. Minn., 1988.
Sturmfels and White, All 11_3 and 12_3 configurations are rational, Aeq. Math., 39 1990 254260.
Von Sterneck, Die Config. 11_3, Monat. f. Math. Phys., 5 325330 1894; Die Config. 12_3, op. cit., 6 223255 1895.
David Wells, Penguin Dictionary of Curious and Interesting Geometry, 1991, p. 72.


EXAMPLE

Example: the Fano plane is the only (7_3) configuration. It contains 7 points 1,2,...7 and 7 triples, 124, 235, 346, 457, 561, 672, 713.
The unique (8_3) configuration consists of the triples 125, 148, 167, 236, 278, 347, 358, 456.
There are three configurations (9_3), one of which is the familiar configuration arising from Desargues's theorem (see Loy illustration).
