In Workstation ArcInfo, the COUNTVERTICES command can be used to write the number of vertices for a line or polygon feature to the attribute table. Instructions provided describe how to do the same in ArcMap.
Right-click the layer and select Open Attribute Table.
Click Options > Add Field to add a new field to the layer.
Name the field NumPoints and select Long Integer for the type.
Right-click the new field and select Field Calculator.
Check the Advanced box.
Copy the following text into the Pre-logic VBA Script Code text box.
Code: Dim pPointCount As IPointCollection Set pPointCount = [SHAPE]