In fact, it preserves each sheet of the two sheeted hyperboloids with fixed positive integral determinant. Any one of these sheets can be taken as a model of the hyperbolic plane, isometric to the Poincaré disk, whose boundary corresponds to the light-cone. In Figure 1 we have shown the fixed points of the simple reflections which generate $W$, the triangular fundamental domain $\cD$ for $W$, and several other reflection lines corresponding to some other positive real roots of $\cF$ which are obtained by applying Weyl group elements to the simple roots. A complete tesselation of the disk would be obtained by including all reflection lines, which are in one-to-one correspondence with all of the positive real roots of $\cF$, $\Phi^+_{real}$. In that tesselation there would be a bijection between the elements of the Weyl group, $W$, and the images of the fundamental domain $\cD$. In Figure 1 we see $\cD$ is the triangle with angles $\pi/2$, $\pi/3$ and $0$, and sides labelled by the simple roots. Six images of $\cD$ form a larger triangle with all vertices on the boundary and all angles zero. The three sides of that larger triangle are labelled $\alpha_1$, $r_0 \alpha_1 = \alpha_1 + 2\alpha_0$ 