[vtkusers] too many points extracted from an unstructured grid

[jean mensa]

Hi all,
I am new to vtk and I am struggling reading points from an
unstructured grid. I use a python code that looks like this,

ugrid = vtk.vtkUnstructuredGrid()
gridreader=vtk.vtkXMLPUnstructuredGridReader()
gridreader.SetFileName(filename)
gridreader.Update()
ugrid=self.gridreader.GetOutput()

this gives me more points and cells then I would expect,

ugrid.GetNumberOfCells()
ugrid.GetNumberOfPoints()

BUT, when I try to get the locations of these points,

vtkPoints = ugrid.GetPoints()
vtkData = vtkPoints.GetData()

I find that many of these points are present multiple times.
Why is that?
How do I extract my points once and only once?

Thank you very much and forgive my ignorance...
j