The configurations 123 revisited


As is known, there are 229 symmetric configurations 123, (Daublebsky von Sterneck in Monatshefte Math Phys 5:223–255, 1895; Gropp in J Comb Inf Syst Sci 15:34–48, 1990). We use tactical decompositions by automorphism group (TDA) to study these configurations in detail. In (Daublebsky von Sterneck in Monatshefte Math Phys 14, 254–260, 1903) the automorphism groups of the configurations were determined. We find some errors there and correct them. For the configurations with a rather big automorphism group, we give models which display the structure of the group.

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Correspondence to Dieter Betten.

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Al-Azemi, A., Betten, D. The configurations 123 revisited. J. Geom. 105, 391–417 (2014).

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Mathematics Subject Classification (2010)

  • 05E18
  • 05XX


  • Configurations
  • tactical decompositions
  • linear spaces