So when you set up the script tool, you can set values to have multiple values rather than creating individual parameters for each point. In which case the end user can add as many points as needed.
When in comes to the geometry, you have to identify the kind of geometry for the script to search for. So for instance:
import arcpy # Create a Describe object from the feature class # desc = arcpy.Describe("C:/data/arch.dgn/Point") # Print some feature class properties # print("Feature Type: " + desc.featureType) print("Shape Type : " + desc.shapeType) print("Spatial Index: " + str(desc.hasSpatialIndex))
the shapeType will tell you what kind of geometry the shape is. Also, as a side note, if you are looking to get X and Y values from the coordinates for/from a shape then it is best to use the separate X and Y shape tokens.
Here is some additional information on how to write geometries.
Hope this helps.