On Near Hexagons and Spreads of Generalized Quadrangles
Bart De Bruyn
DOI: 10.1023/A:1008709716107
Abstract
The glueing-construction described in this paper makes use of two generalized quadrangles with a spread in each of them and yields a partial linear space with special properties. We study the conditions under which glueing will give a near hexagon. These near hexagons satisfy the nice property that every two points at distance 2 are contained in a quad. We characterize the class of the 
glued near hexagons 
and give examples, some of which are new near hexagons.
glued near hexagons and give examples, some of which are new near hexagons.Pages: 211–226
Keywords: spread; generalized quadrangle; near polygon
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References
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3. A.E. Brouwer and H.A. Wilbrink, “The structure of near polygons with quads,” Geom. Dedicata 14 (1983), 145-176.
4. B. De Bruyn and F. De Clerck, “On linear representations of near hexagons,” European J. Combin. 20 (1999), 45-60.
5. M. Hall, Jr., “Affine generalized quadrilaterals,” Studies in Pure Mathematics, Academic Press, London, 1971, pp. 113-116.
6. S.E. Payne and J.A. Thas, Finite Generalized Quadrangles, Pitman, Boston,
1984. Research Notes in Mathematics, vol. 110.
7. S.A. Shad and E.E. Shult, “The near n-gon geometries,” Unpublished, 1979.
8. E.E. Shult and A. Yanushka, “Near n-gons and line systems,” Geom. Dedicata 9 (1980), 1-72.