Solution
= Solution
If six triangles met at every vertex, counting vertex-face incidences would give $3F=6V$, hence $F=2V$. But part b gives $F=2V-4$, a contradiction. Therefore \b[no such triangulation exists].
= Solution
If six triangles met at every vertex, counting vertex-face incidences would give $3F=6V$, hence $F=2V$. But part b gives $F=2V-4$, a contradiction. Therefore \b[no such triangulation exists].