Some Constructions and Embeddings of the Tilde Geometry


Some old and new onstructions of the tilde geometry (the flag transitive connected triple cover of the unique generalized quadrangle  W(2) of order  (2 ,2)) are discussed. Using them,we prove some properties of that geometry.In particular,we compute its generating rank,we give an explicit description of its universal projective embedding and we determine its homogeneous embeddings.

DOI Code: 10.1285/i15900932v21n2p1

Keywords: Generalized quadrangle; Diagram geometry; Tilde geometry; Triple cover; Universal embedding

Classification: 51E12; 51E24

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