diff --git a/src/sage/geometry/polyhedron/base.py b/src/sage/geometry/polyhedron/base.py
index 022d31fb314..aca0c7bed18 100644
--- a/src/sage/geometry/polyhedron/base.py
+++ b/src/sage/geometry/polyhedron/base.py
@@ -2804,6 +2804,30 @@ def normal_fan(self, direction='inner'):
             ...
             NotImplementedError: normal fan handles only polytopes over the rationals
 
+            sage: P = Polyhedron(vertices=[[0,0],[2,0],[0,2],[2,1],[1,2]])
+            sage: P.normal_fan(direction=None)
+            Traceback (most recent call last):
+            ...
+            TypeError: the direction should be `inner` or `outer`
+
+            sage: inner_nf = P.normal_fan()
+            sage: inner_nf.rays()
+            N( 1,  0),
+            N( 0, -1),
+            N( 0,  1),
+            N(-1,  0),
+            N(-1, -1)
+            in 2-d lattice N
+
+            sage: outer_nf = P.normal_fan(direction='outer')
+            sage: outer_nf.rays()
+            N( 1,  0),
+            N( 1,  1),
+            N( 0,  1),
+            N(-1,  0),
+            N( 0, -1)
+            in 2-d lattice N
+
         REFERENCES:
 
         For more information, see Chapter 7 of [Zie2007]_.