Colouring the rational quantum sphere and the Kochen-Specker theorem

We review and extend recent findings of Godsil and Zaks, who published a constructive colouring of the rational unit sphere with the property that for any orthogonal tripod formed by rays extending from the origin of the points of the sphere, exactly one ray is red, one white and one black. They also showed that any consistent colouring of the real sphere requires an additional colour. We discuss some of the consequences for the Kochen-Specker theorem.