Figure 1

The K -triangulation of 2-simplex$\mathit{S}\mathbf{=}\mathbf{〈}{\mathit{v}}^{\mathbf{1}}\mathbf{,}{\mathit{v}}^{\mathbf{2}}\mathbf{,}{\mathit{v}}^{\mathbf{3}}\mathbf{〉}$with grid size 6. The small triangles are members of the triangulation $K(S,6)$. The number at a vertex of a simplex in $K(S,6)$ is the value of l assigned to the vertex and one sees that l satisfies the assumptions of Lemma 1. The sequence of simplices ${\sigma }_1,\dots ,{\sigma }_{12}$ meets the requirements described in the proof of Lemma 1.