Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 39, No. 1, pp. 135-153 (1998)

Plane Models of Semi-biplanes

B. Polster; A. E. Schroth

Department of Pure Mathematics, University of Adelaide
Adelaide, South Australia 5005,Australia
Institut für Topologie, TU Braunschweig
Pockelsstr. 14, D-38106 Braunschweig, Germany

Abstract: The connection between semi-biplanes and antiregular generalized quadrangles is employed to construct different plane models of semi-biplanes. The connection between antiregular generalized quadrangles and circle planes is used to generalize these models. The plane models of the classical semi-biplane are described explicitely. They can be visualized easily. The treatment shows how the different models are connected.

Keywords: Semi-biplanes, generalized quadrangles, antiregular quadrangles, circle planes

Classification (MSC91): 51A50, 51E12, 51B05, 51H15.

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