||This is indeed a problem. If you have two points with exactly the same coordinates, the tool won't work. You have to delete the duplicates.
We have used another way, without deleting. We have three points with exactly the same coordinates. Every point has a different azimut angle. We slightly move the points in the direction of the azimut angle, lets say only some centimeters. Then the creation of Thiessen polygons work.
The procedure of shifting the points in the direction of their azimut is written in C#.
Best regards, Stefan