thanks for your response. In other contexts, the terms vertex and point are used interchangeably, so it helps to know that the Esri documentation on this tool only uses the term 'vertices' to refer to line segment/polygon edge endpoints.
What I'm really trying to find out is if this tool ever gives anything other than an empty table. I'm looking for a sample broken dataset to see the Check Geometry in action. I have tried to create some 'errors' (e.g., bow-tie polygons), but I can seem to get any response from this tool.
Have any of you come across a dataset that gives more than an empty table?
Do any of you have on hand a sample dataset (that you could share) that gives more than an empty table?