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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. A generalized quadrangle is an incidence structure. A generalized quadrangle is by definition a polar space of rank two. They are the generalized n-gons with n = 4. They are also precisely the partial geometries pg(s,t, ).If (P,B,I) is a generalized quadrangle with parameters ''(s,t)'', then (B,P,I 1), with I 1 the inverse incidence relation, is also a generalized quadrangle. This is the dual generalized quadrangle. Its parameters are ''(t,s)''. Even if s = t, the dual structure need not be isomorphic with the original structure.