Delete Vertex 
Delete a Vertex
Use the Delete Vertex option to remove a vertex from a triangulation. The triangles containing the vertex being deleted will automatically be removed from the triangulation.
Figure 1: The Original Triangulation
Figure 2: After a Vertex has been Deleted
Instructions
On the Model menu, point to Triangle Surface, and then click Delete Vertex.
Select the triangulation. The triangulation model will be selected automatically if there is only one loaded onscreen.
Select the vertex that you want to delete. Use the Snap to Objects or
Snap to Points modes to ensure accurate selection. You will then need to confirm that the correct vertex was selected.
Select the next vertex to delete. Cancel when you have finished removing vertices.