diff --git a/src/sage/geometry/fan.py b/src/sage/geometry/fan.py
index af3935741b8..c0e0644be4c 100644
--- a/src/sage/geometry/fan.py
+++ b/src/sage/geometry/fan.py
@@ -646,7 +646,8 @@ def result():
             rays = new_rays
         else:
             rays = tuple(sorted(ray_set))
-        cones = (tuple(sorted(rays.index(ray) for ray in cone.rays()))
+        ray_to_index = {ray: i for i, ray in enumerate(rays)}
+        cones = (tuple(sorted(ray_to_index[ray] for ray in cone.rays()))
                  for cone in cones)
         return result()
     # Construct the fan from rays and "tuple cones"
@@ -1925,7 +1926,8 @@ def _subdivide_stellar(self, new_rays, verbose):
         new_fan_rays = list(self.rays())
         new_fan_rays.extend(ray for ray in new_rays
                                 if ray not in self.rays().set())
-        cones = tuple(tuple(sorted(new_fan_rays.index(ray) for ray in cone))
+        ray_to_index = {ray: i for i, ray in enumerate(new_fan_rays)}
+        cones = tuple(tuple(sorted(ray_to_index[ray] for ray in cone))
                       for cone in cones)
         fan = Fan(cones, new_fan_rays, check=False, normalize=False)
         return fan
diff --git a/src/sage/geometry/hyperplane_arrangement/library.py b/src/sage/geometry/hyperplane_arrangement/library.py
index 0c5f67b546e..cfa2fbeb083 100644
--- a/src/sage/geometry/hyperplane_arrangement/library.py
+++ b/src/sage/geometry/hyperplane_arrangement/library.py
@@ -152,9 +152,10 @@ def bigraphical(self, G, A=None, K=QQ, names=None):
         H = make_parent(K, n, names)
         x = H.gens()
         hyperplanes = []
-        for e in G.edges(sort=True):
-            i = G.vertices(sort=True).index(e[0])
-            j = G.vertices(sort=True).index(e[1])
+        vertex_to_int = {u: i for i, u in enumerate(G)}
+        for u, v in G.edge_iterator(labels=False, sort_vertices=False):
+            i = vertex_to_int[u]
+            j = vertex_to_int[v]
             hyperplanes.append( x[i] - x[j] - A[i][j])
             hyperplanes.append(-x[i] + x[j] - A[j][i])
         return H(*hyperplanes)
@@ -264,9 +265,10 @@ def G_semiorder(self, G, K=QQ, names=None):
         H = make_parent(K, n, names)
         x = H.gens()
         hyperplanes = []
-        for e in G.edges(sort=True):
-            i = G.vertices(sort=True).index(e[0])
-            j = G.vertices(sort=True).index(e[1])
+        vertex_to_int = {u: i for i, u in enumerate(G.vertices(sort=True))}
+        for u, v in G.edge_iterator(labels=False):
+            i = vertex_to_int[u]
+            j = vertex_to_int[v]
             hyperplanes.append(x[i] - x[j] - 1)
             hyperplanes.append(x[i] - x[j] + 1)
         return H(*hyperplanes)
@@ -303,9 +305,10 @@ def G_Shi(self, G, K=QQ, names=None):
         H = make_parent(K, n, names)
         x = H.gens()
         hyperplanes = []
-        for e in G.edges(sort=True):
-            i = G.vertices(sort=True).index(e[0])
-            j = G.vertices(sort=True).index(e[1])
+        vertex_to_int = {u: i for i, u in enumerate(G.vertices(sort=True))}
+        for u, v in G.edge_iterator(labels=False):
+            i = vertex_to_int[u]
+            j = vertex_to_int[v]
             hyperplanes.append(x[i] - x[j])
             hyperplanes.append(x[i] - x[j] - 1)
         return H(*hyperplanes)
@@ -351,9 +354,10 @@ def graphical(self, G, K=QQ, names=None):
         H = make_parent(K, n, names)
         x = H.gens()
         hyperplanes = []
-        for e in G.edges(sort=True):
-            i = G.vertices(sort=True).index(e[0])
-            j = G.vertices(sort=True).index(e[1])
+        vertex_to_int = {u: i for i, u in enumerate(G.vertices(sort=True))}
+        for u, v in G.edge_iterator(labels=False):
+            i = vertex_to_int[u]
+            j = vertex_to_int[v]
             hyperplanes.append(x[i] - x[j])
         A = H(*hyperplanes)
         charpoly = G.chromatic_polynomial()
diff --git a/src/sage/geometry/lattice_polytope.py b/src/sage/geometry/lattice_polytope.py
index c7c53a65045..48758580ec6 100644
--- a/src/sage/geometry/lattice_polytope.py
+++ b/src/sage/geometry/lattice_polytope.py
@@ -1566,7 +1566,8 @@ def ambient_point_indices(self):
         if self._ambient is self:
             return tuple(range(self.npoints()))
         points = self._ambient.points()
-        return tuple(points.index(p) for p in self.points())
+        point_to_index = {p: i for i, p in enumerate(points)}
+        return tuple(point_to_index[p] for p in self.points())
 
     @cached_method
     def ambient_ordered_point_indices(self):
@@ -1600,7 +1601,8 @@ def ambient_ordered_point_indices(self):
         if self._ambient is self:
             return tuple(range(self.npoints()))
         points = self._ambient.points()
-        return tuple(points.index(p) for p in sorted(self.points()))
+        point_to_index = {p: i for i, p in enumerate(points)}
+        return tuple(point_to_index[p] for p in sorted(self.points()))
 
     def ambient_vertex_indices(self):
         r"""
@@ -3614,8 +3616,9 @@ def plot3d(self,
             elif dim == 3:
                 if facet_colors is None:
                     facet_colors = [facet_color] * self.nfacets()
+                vertex_to_index = {v: i for i, v in enumerate(self.vertices())}
                 for f, c in zip(self.facets(), facet_colors):
-                    pplot += IndexFaceSet([[self.vertices().index(v) for v in f.vertices(f.traverse_boundary())]],
+                    pplot += IndexFaceSet([[vertex_to_index[v] for v in f.vertices(f.traverse_boundary())]],
                         vertices, opacity=facet_opacity, rgbcolor=c)
         if show_edges:
             if dim == 1:
@@ -4081,7 +4084,8 @@ def traverse_boundary(self):
             if next == l[-2]:
                 next = prev
             l.append(next)
-        return [self.vertices().index(v.vertex(0)) for v in l]
+        vertex_to_index = {v: i for i, v in enumerate(self.vertices())}
+        return [vertex_to_index[v.vertex(0)] for v in l]
 
     def vertex(self, i):
         r"""
diff --git a/src/sage/geometry/polyhedron/plot.py b/src/sage/geometry/polyhedron/plot.py
index df157066c43..2c959b61195 100644
--- a/src/sage/geometry/polyhedron/plot.py
+++ b/src/sage/geometry/polyhedron/plot.py
@@ -1816,9 +1816,10 @@ def _tikz_3d_in_3d(self, view, angle, scale, edge_color,
 
         # Draw the facets in the front by going in cycles for every facet.
         tikz_pic += '%%\n%%\n%% Drawing the facets\n%%\n'
+        vertex_to_index = {v: i for i, v in enumerate(vertices)}
         for index_facet in front_facets:
             cyclic_vert = cyclic_sort_vertices_2d(list(facets[index_facet].incident()))
-            cyclic_indices = [vertices.index(v) for v in cyclic_vert]
+            cyclic_indices = [vertex_to_index[v] for v in cyclic_vert]
             tikz_pic += '\\fill[facet] '
             for v in cyclic_indices:
                 if v in dict_drawing:
diff --git a/src/sage/geometry/polyhedron/ppl_lattice_polytope.py b/src/sage/geometry/polyhedron/ppl_lattice_polytope.py
index 5698d71a045..d45f8a3991a 100644
--- a/src/sage/geometry/polyhedron/ppl_lattice_polytope.py
+++ b/src/sage/geometry/polyhedron/ppl_lattice_polytope.py
@@ -671,7 +671,8 @@ def pointsets_mod_automorphism(self, pointsets):
         points = tuple(sorted(points))
         Aut = self.lattice_automorphism_group(points,
                                               point_labels=tuple(range(len(points))))
-        indexsets = set(frozenset(points.index(p) for p in ps)
+        point_to_index = {p: i for i, p in enumerate(points)}
+        indexsets = set(frozenset(point_to_index[p] for p in ps)
                         for ps in pointsets)
         orbits = []
         while indexsets: