Abstract
We prove that the geometry of vertices, edges and qn-cliques of the graph Alt(n+1,q) of (n+1)-dimensional alternating forms over GF(q), n≥4, is the unique flag-transitive geometry of rank 3 where planes are isomorphic to the point-line system of AG(n,q) and the star of a point is dually isomorphic to a projective space.
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