Split semi-biplanes in antiregular generalized quadrangles

Burkard Polster, Andreas E. Schroth

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There are a number of important substructures associated with sets of points of antiregular quadrangles. Inspired by a construction of P. Wild, we associate with any four distinct collinear points p, q, r and s of an antiregular quadrangle an incidence structure which is the union of the two biaffine planes associated with {p, r} and {q, s}. We investigate when this incidence structure is a semi-biplane.

Original languageEnglish
Pages (from-to)625-637
Number of pages13
JournalBulletin of the Belgian Mathematical Society - Simon Stevin
Issue number5
Publication statusPublished - Dec 1997
Externally publishedYes


  • Antiregular quadrangles
  • Generalized quadrangles
  • Semi-biplanes

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