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Some constructions and embeddings of the tilde geometry. (English) Zbl 1171.51302

Summary: Some old and new constructions 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.

MSC:

51E12 Generalized quadrangles and generalized polygons in finite geometry
51E24 Buildings and the geometry of diagrams
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