The clique number C of a graph is the largest clique size in the graph. For a random geometric graph of n vertices, taken uniformly at random, including an edge beween two vertices if their distance, taken with the uniform norm, is less than a parameter r on a torus Tda, we find the asymptotic behaviour of the clique number. Setting θ = (r)d, in the a subcritical regime where θ = o( 1 ), we exhibit the intervals of θ where C n takes the same value asymptotically almost surely. In the critical regime, θ ∼ 1 , we show that C is growing slightly slower than ln n asymptotically n almost surely. Finally, in the supercritical regime, 1 = o(θ), we prove n that C grows as nθ asymptotically almost surely. We also investigate the behaviour of related graph characteristics: the chromatic number, the maximum vertex degree, and the independence number.