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The two spaces combine into a 10-D discrete space-time obeying the discrete symmetry transformations of "Weyl" SO(9,1) = Weyl [E.
As we have seen, gauge symmetries are guaranteed by introducing connections on the relevant fibre bundles, which serve to spread the conventional choice of representation of the matter field across spacetime, so tying together the local symmetry transformations, at different spacetime points.
In our discrete 4-D spacetime we need to tesselate this Riemann surface into identical equilateral triangles and then perform the symmetry transformations of the sphere.