Compatible spreads of symmetry in near polygons

In De Bruyn [7] it was shown that spreads of symmetry of near polygons give rise to many other near polygons, the so-called glued near polygons. In the present paper we will study spreads of symmetry in product and glued near polygons. Spreads of symmetry in product near polygons do not lead to new glued near polygons. The study of spreads of symmetry in glued near polygons gives rise to the notion of ‘compatible spreads of symmetry’. We will classify all pairs of compatible spreads of symmetry for the known classes of dense near polygons. All these pairs of spreads can be used to construct new glued near polygons.