diff --git a/masque/utils/vertices.py b/masque/utils/vertices.py
index c4a7cb6..176f0f5 100644
--- a/masque/utils/vertices.py
+++ b/masque/utils/vertices.py
@@ -18,10 +18,16 @@ def remove_duplicate_vertices(vertices: ArrayLike, closed_path: bool = True) ->
         `vertices` with no consecutive duplicates. This may be a view into the original array.
     """
     vertices = numpy.asarray(vertices)
+    if vertices.shape[0] <= 1:
+        return vertices
     duplicates = (vertices == numpy.roll(vertices, -1, axis=0)).all(axis=1)
     if not closed_path:
         duplicates[-1] = False
-    return vertices[~duplicates]
+
+    result = vertices[~duplicates]
+    if result.shape[0] == 0 and vertices.shape[0] > 0:
+        return vertices[:1]
+    return result
 
 
 def remove_colinear_vertices(vertices: ArrayLike, closed_path: bool = True) -> NDArray[numpy.float64]: