diff --git a/src/doc/en/reference/references/index.rst b/src/doc/en/reference/references/index.rst
index 4c9c2fd1ab4..018c993a57d 100644
--- a/src/doc/en/reference/references/index.rst
+++ b/src/doc/en/reference/references/index.rst
@@ -1645,9 +1645,12 @@ REFERENCES:
              constrained optimization. ACM Transactions on
              Mathematical Software, Vol 23, Num. 4, pp.550--560, 1997.
 
-.. [Zie1998] G. Ziegler. *Shelling polyhedral 3-balls and
+.. [Zie1998] G. M. Ziegler. *Shelling polyhedral 3-balls and
              4-polytopes*. Discrete Comput. Geom. 19 (1998), 159-174.
 
+.. [Zie2007] G. M. Ziegler. *Lectures on polytopes*, Volume
+             152 of Graduate Texts in Mathematics, 7th printing of 1st edition, Springer, 2007.
+
 .. [Zor2008] \A. Zorich "Explicit Jenkins-Strebel representatives of
              all strata of Abelian and quadratic differentials",
              Journal of Modern Dynamics, vol. 2, no 1, 139-185 (2008)
diff --git a/src/sage/geometry/polyhedron/base.py b/src/sage/geometry/polyhedron/base.py
index 5f7421b8ba4..5e68649aa2a 100644
--- a/src/sage/geometry/polyhedron/base.py
+++ b/src/sage/geometry/polyhedron/base.py
@@ -2268,6 +2268,48 @@ def gale_transform(self):
         A_ker = A.right_kernel()
         return A_ker.basis_matrix().transpose().rows()
 
+    @cached_method
+    def normal_fan(self):
+        r"""
+        Return the normal fan of a compact full-dimensional rational polyhedron.
+
+        OUTPUT:
+
+        A complete fan of the ambient space as a
+        :class:`~sage.geometry.fan.RationalPolyhedralFan`.
+
+        .. SEEALSO::
+
+            :meth:`~sage.geometry.polyhedron.base.face_fan`.
+
+        REFERENCES:
+
+        For more information, see Chapter 7 of [Zie2007]_.
+        """
+
+        return NormalFan(self)
+
+    @cached_method
+    def face_fan(self):
+        r"""
+        Return the face fan of a compact full-dimensional rational polyhedron.
+
+        OUTPUT:
+
+        A complete fan of the ambient space as a
+        :class:`~sage.geometry.fan.RationalPolyhedralFan`.
+        
+        .. SEEALSO::
+
+            :meth:`~sage.geometry.polyhedron.base.normal_fan`.
+
+        REFERENCES:
+
+        For more information, see Chapter 7 of [Zie2007]_.
+        """
+
+        return FaceFan(self)
+
     def triangulate(self, engine='auto', connected=True, fine=False, regular=None, star=None):
         r"""
         Returns a triangulation of the polytope.