Geometric Configurations

  • Tomaž Pisanski
  • Brigitte Servatius
Part of the Birkhäuser Advanced Texts Basler Lehrbücher book series (BAT)


A geometric configuration is regarded as a representation of a combinatorial configuration into a geometric space. In this chapter we introduce the most important ambient spaces, the real and projective spaces, and consider representations, both obvious and surprising, of the classical combinatorial configurations, and considering which of these realizations are autopolar. The highlight of this chapter is a discussion of what we call the “Grünbaum” incidence calculus, a summary of the methods which Grünbaum has developed to construct projective realizations of combinatorial configurations. The chapter ends with a summary of relatively recent results on a collection of projective configurations having a cyclic action, called polycyclic configurations.


Projective Plane Cayley Graph White Vertex Incidence Structure Affine Plane 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Tomaž Pisanski
    • 1
  • Brigitte Servatius
    • 2
  1. 1.IMFM Oddelek za Teoretično RačunalništvoUniverza v LjubljaniLjubljanaSlovenia
  2. 2.Department of MathematicsWorcester Polytechnic InstituteWorcesterUSA

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