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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, ). A figure may look like a graph, but in a graph an edge has just two ends (beyond a vertex a new edge starts), while a line in an incidence structure can be incident to more points. An incidence structure has no concept of a point being in between two other points; the order of points on a line is undefined. Compare with ordered geometry, which does have a notion of betweenness.
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