documentated that backend field is fast

src/sage/geometry/polyhedron/library.py

@@ -2520,6 +2520,15 @@ def permutahedron(self, n, project=False, backend=None):
             sage: perm4.graph().is_isomorphic(graphs.BubbleSortGraph(4))
             True
 
+        As both Hrepresentation an Vrepresentation are known, the permutahedron can be set
+        up with both using the backend ``field``. The following takes very very long time
+        to recompute, e.g. with backend ``ppl``::
+
+            sage: polytopes.permutahedron(8, backend='field')  # (~1s)
+            A 7-dimensional polyhedron in QQ^8 defined as the convex hull of 40320 vertices
+            sage: polytopes.permutahedron(9, backend='field')  # long time -- (~5s)
+            A 8-dimensional polyhedron in QQ^9 defined as the convex hull of 362880 vertices
+
         .. SEEALSO::
 
             * :meth:`~sage.graphs.graph_generators.GraphGenerators.BubbleSortGraph`