The point \(X\) of a generalized quadrangle (GQ) of order \((s,t)\) is regular if \(|(\{X,Y\}^\bot)^\bot|=t+1\) for every point \(Y\) not collinear with \(X\). Let the generalized quadrangle \(\mathcal S\) of order \((s,t)\) contain a regular point \(X\). Then the incidence structure \({\mathcal N}_X\) with pointset \(X^\bot-\{X\}\), with lineset \(\{(\{Y,Z\}^\bot)^\bot\;|\;Y,Z\in X^\bot-\{X\}, Y\not\sim Z\}\), and with natural incidence, is the dual of a net of order \(s\) and degree \(t+1\) (Theorem 6). If \(\Gamma\) is a point graph of a point-line geometry \({\mathcal N}=({\mathcal P}, {\mathcal L},I)\) and the \(t\)-fold cover \((\bar \Gamma,p)\) satisfies \((*)\) for any line \(l\in {\mathcal L}\), if \({\mathcal P}_l=\{P\in {\mathcal P}\;|\;PIl\}\), then \(p^{-1}({\mathcal P}_l)\) consists of \(t\) disjoint complete graphs, then we can form a geometry with points the vertices of \(\bar \Gamma\), and lines defined to be the set of complete graphs of \((*)\). Let \({\mathcal N}=({\mathcal P},{\mathcal L},I)\) be a point-line geometry with point graph \(\Gamma\). A \(t\)-fold cover of \(\mathcal N\) is a pair \((\bar {\mathcal N},p)\), where \(\bar {\mathcal N}=(\bar {\mathcal P},\bar {\mathcal L},I)\) is a point-line geometry with point graph \(\bar \Gamma\) and \(p:\bar {\mathcal P}\to {\mathcal P}\) such that \((\bar \Gamma,p)\) is a \(t\)-fold cover of \(\Gamma\) and \((\bar \Gamma,p)\) satisfies \((*)\) giving rise to the geometry \(\bar {\mathcal N}\). Let \({\mathcal S}=({\mathcal P},{\mathcal L},I)\) be a GQ of order \((s,t)\) with regular point \(X\) and associated net \({\mathcal N}_X\). Then \((\bar {\mathcal N}_X,p)\) with \(\bar {\mathcal P}_X={\mathcal P}-X^\bot\), \(\bar {\mathcal L}={\mathcal L}-\{l\in {\mathcal L}\;|\;lIX\}\) and \(\bar I_X\) induced by \(I\), together with \(p:Y\mapsto \{X,Y\}^\bot\) for \(Y\in \bar {\mathcal P}\), is a \(t\)-fold cover of \({\mathcal N}_X\) (Theorem 16). There are some applications to subquadrangles of GQs with a regular point (\S\ 6) and representing GQs with abelian centre of symmetry (\S\ 7).