The Möbius-Kantor configuration is the unique configuration. It is transitive
and self-dual. While it is realizable over the complex numbers, is cannot be realized
over the real or rational numbers (Gropp 1997). Its incidence
structure is illustrated above using a circle in addition to seven lines.
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and Regular Graphs." Bull. Amer. Math. Soc.56, 413-455, 1950.Gropp,
H. "Configurations and Their Realization." Discr. Math.174,
137-151, 1997.Grünbaum, B. Configurations
of Points and Lines. Providence, RI: Amer. Math. Soc., pp. 67-68, 2009.Pisanski,
T. and Randić, M. "Bridges between Geometry and Graph Theory." In
Geometry
at Work: A Collection of Papers Showing Applications of Geometry (Ed. C. A. Gorini).
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configuration. It is transitive
and self-dual. While it is realizable over the complex numbers, is cannot be realized
over the real or rational numbers (Gropp 1997). Its incidence
structure is illustrated above using a circle in addition to seven lines.
