The XY pairs which make up the vertices of a polygon are within the paths of ring features in the geometry properties. Given you do not have a license to run Feature Vertices to Points, you will need to access the geometry properties of the feature in order to capture the coordinate values. Once you have the coordinate values, they can be displayed in a number of ways. To access the geometry properties, you can use the data access (da) module of arcpy, to cursor through each feature, and then loop through the rings and paths of each geometry object (Shape field).
with arcpy.da.SearchCursor(in_fc, [OID@", "SHAPE@"]) as sc:
for row in sc:
feature_id = row[0]
polygon_geometry = row[1]
With the geometry object in hand, you can then read the geometries.
for part in polygon_geometry:
for pnt in part:
if pnt:
print("{}, {}".format(pnt.X, pnt.Y))
Now that you have access to the coordinates and ID for each polygon, you could easily build a table with the coordinate values and store the ID value to later reference the Polygon feature class to possibly label each vertex, or display as part of the feature's pop-up, etc.
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tag refers to the HTTP POST method.