The Structure of Near Polygons with Quads

摘要

A structure theory for near polygons with quads was developed. Lemmas are proved for thick near polygons and for thin near polygons with parameters (s, t2, t3..., td) and diameter d. It is shown that, if a thick near polygon has quads, it contains sub 2j-gons for 2 equal to or j equal, to or d. Using inequalities obtained by eigenvalue techniques and by structural considerations, it is proved that there are only very few possibilities for the parameter set of a regular near polygon. Regular sporadic 2d-gons do not exist for d equal to or 4 with 51 and t21, and t3 different from t2 x (t2 + 1).