The Non-Existence of certain Regular Generalized Polygons
نویسنده
چکیده
We define the notion of d i -regularity and regularity in generalized polygons, thus generalizing the notion of ‘regular point’ in a generalized quadrangle or hexagon. We show that a thick generalized polygon cannot contain too many regular points unless it is a projective plane, quadrangle or hexagon. For certain polygons (thick ‘odd’gons and 8-gons), we show that even a certain number of d2-regular points cannot exist. As an application, we present a geometric and rather elementary proof of the non-existence of thick buildings of spherical type H3.
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