This paper is devoted to the study of the graph sequence G_n=(V_n,E_n), where V_n is the set of all vectors v∈Rⁿ with coordinates in {−1,0,1} such that |v|=3 and E_n consists of all pairs of vertices with scalar product 1. We find the exact value of the independence number of G_n. As a corollary we get new lower bounds on χ(Rⁿ) and χ(Qⁿ) for small values of n.