diff --git a/src/sage/geometry/polyhedron/base3.py b/src/sage/geometry/polyhedron/base3.py
index 2f056dee15b..615816476e2 100644
--- a/src/sage/geometry/polyhedron/base3.py
+++ b/src/sage/geometry/polyhedron/base3.py
@@ -967,7 +967,7 @@ def vertex_adjacency_matrix(self):
     @cached_method
     def facet_adjacency_matrix(self):
         """
-        Return the adjacency matrix for the facets and hyperplanes.
+        Return the adjacency matrix for the facets.
 
         EXAMPLES::
 
@@ -979,6 +979,13 @@ def facet_adjacency_matrix(self):
             [1 1 1 0 1]
             [1 1 1 1 0]
 
+            sage: p = Polyhedron(vertices=[(0,0),(1,0),(0,1)])
+            sage: p.facet_adjacency_matrix()
+            [0 1 1]
+            [1 0 1]
+            [1 1 0]
+
+
         The facet adjacency matrix has base ring integers. This way one can express various
         counting questions::
 
@@ -992,52 +999,18 @@ def facet_adjacency_matrix(self):
 
         Check that :trac:`28828` is fixed::
 
-                sage: s4.facet_adjacency_matrix().is_immutable()
-                True
-        """
-        return self._facet_adjacency_matrix()
-
-    def _facet_adjacency_matrix(self):
-        """
-        Compute the facet adjacency matrix in case it has not been
-        computed during initialization.
-
-        EXAMPLES::
-
-            sage: p = Polyhedron(vertices=[(0,0),(1,0),(0,1)])
-            sage: p._facet_adjacency_matrix()
-            [0 1 1]
-            [1 0 1]
-            [1 1 0]
+            sage: s4.facet_adjacency_matrix().is_immutable()
+            True
 
         Checks that :trac:`22455` is fixed::
 
             sage: s = polytopes.simplex(2)
-            sage: s._facet_adjacency_matrix()
+            sage: s.facet_adjacency_matrix()
             [0 1 1]
             [1 0 1]
             [1 1 0]
-
         """
-        # TODO: This implementation computes the whole face lattice,
-        # which is much more information than necessary.
-        M = matrix(ZZ, self.n_facets(), self.n_facets(), 0)
-        codim = self.ambient_dim()-self.dim()
-
-        def set_adjacent(h1, h2):
-            if h1 is h2:
-                return
-            i = h1.index() - codim
-            j = h2.index() - codim
-            M[i, j] = 1
-            M[j, i] = 1
-
-        for face in self.faces(self.dim()-2):
-            Hrep = face.ambient_Hrepresentation()
-            assert(len(Hrep) == codim+2)
-            set_adjacent(Hrep[-2], Hrep[-1])
-        M.set_immutable()
-        return M
+        return self.combinatorial_polyhedron().facet_adjacency_matrix()
 
     def a_maximal_chain(self):
         r"""
diff --git a/src/sage/geometry/polyhedron/combinatorial_polyhedron/base.pyx b/src/sage/geometry/polyhedron/combinatorial_polyhedron/base.pyx
index 6e795febc0e..fc0bb11ca9c 100644
--- a/src/sage/geometry/polyhedron/combinatorial_polyhedron/base.pyx
+++ b/src/sage/geometry/polyhedron/combinatorial_polyhedron/base.pyx
@@ -1467,6 +1467,51 @@ cdef class CombinatorialPolyhedron(SageObject):
             return tuple((facet_one(i), facet_two(i))
                          for i in range(n_ridges))
 
+    @cached_method
+    def facet_adjacency_matrix(self):
+        """
+        Return the binary matrix of facet adjacencies.
+
+        .. SEEALSO::
+
+            :meth:`~sage.geometry.polyhedron.base.Polyhedron_base.vertex_adjacency_matrix`.
+
+        EXAMPLES::
+
+            sage: P = polytopes.cube()
+            sage: C = P.combinatorial_polyhedron()
+            sage: C.facet_adjacency_matrix()
+            [0 1 1 0 1 1]
+            [1 0 1 1 1 0]
+            [1 1 0 1 0 1]
+            [0 1 1 0 1 1]
+            [1 1 0 1 0 1]
+            [1 0 1 1 1 0]
+
+        TESTS::
+
+            sage: CombinatorialPolyhedron(-1).facet_adjacency_matrix()
+            []
+            sage: CombinatorialPolyhedron(0).facet_adjacency_matrix()
+            []
+            sage: polytopes.cube().facet_adjacency_matrix().is_immutable()
+            True
+        """
+        from sage.rings.integer_ring import ZZ
+        from sage.matrix.constructor import matrix
+        cdef Matrix_integer_dense adjacency_matrix = matrix(
+                ZZ, self.n_facets(), self.n_facets(), 0)
+        cdef size_t i, a, b
+
+        self._compute_ridges(-1)
+        for i in range(self._n_ridges):
+            a = self._get_edge(self._ridges, i, 0)
+            b = self._get_edge(self._ridges, i, 1)
+            adjacency_matrix.set_unsafe_si(a, b, 1)
+            adjacency_matrix.set_unsafe_si(b, a, 1)
+        adjacency_matrix.set_immutable()
+        return adjacency_matrix
+
     def facet_graph(self, names=True):
         r"""
         Return the facet graph.