Tilings of the hyperbolic space and Lipschitz functions

We use a special tiling for the hyperbolic d-space H-d for d=2,3,4 to construct an (almost) explicit isomorphism between the Lipschitz-free space F(H-d) and F(P)circle plus F(N), where P is a polytope in R-d and N a net in H(d )coming from the tiling. This implies that the spaces F(H-d) and F(R-d)circle plus F(M) are isomorphic for every net M in H-d. In particular, we obtain that, for d=2,3,4, F(H-d) has a Schauder basis. Moreover, using a similar method, we also give an explicit isomorphism between Lip(H-d) and Lip(R-d).