Figure 1

Illustration of Lemma 2 for \(\pmb{n=3}\) . Small triangles are members of a triangulation T of \(\langle{v^{1},v^{2},v^{3}} \rangle\). The triangulation T satisfies the assumptions of the lemma. The number at a vertex of a simplex in T is the value of the function l assigned to the vertex, and it is clear that l satisfies the assumptions of Lemma 2. The sequence of simplices \(\sigma_{1},\ldots,\sigma_{11}\) is constructed according to the rules presented in the proof of Lemma 2.