diff --git a/masque/shapes/polygon.py b/masque/shapes/polygon.py
index cbcbe63..1e0352f 100644
--- a/masque/shapes/polygon.py
+++ b/masque/shapes/polygon.py
@@ -20,7 +20,7 @@ class Polygon(Shape):
     A polygon, consisting of a bunch of vertices (Nx2 ndarray) which specify an
        implicitly-closed boundary, and an offset.
 
-    Note that the setter for `Polygon.vertices` creates a copy of the
+    Note that the setter for `Polygon.vertices` may creates a copy of the
       passed vertex coordinates.
 
     A `normalized_form(...)` is available, but can be quite slow with lots of vertices.
@@ -379,9 +379,8 @@ class Polygon(Shape):
     def normalized_form(self, norm_value: float) -> normalized_shape_tuple:
         # Note: this function is going to be pretty slow for many-vertexed polygons, relative to
         #   other shapes
-        meanv = self.vertices.mean(axis=0)
-        zeroed_vertices = self.vertices - meanv
-        offset = meanv + self.offset
+        offset = self.vertices.mean(axis=0) + self.offset
+        zeroed_vertices = self.vertices - offset
 
         scale = zeroed_vertices.std()
         normed_vertices = zeroed_vertices / scale