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A unit distance graph is a finite simple graph which may be drawn on the plane so that its vertices are represented by distinct points and the edges are represented by closed line segments of unit length. In this paper, we show that the only primitive strongly regular unit distance graphs are \((i)\) the pentagon, \((ii)\) \(K_3 \times K_3\), \((iii)\) the Petersen graph, and \((iv)\) possibly the Hoffman-Singleton graph.