more examples and fix docstring

src/sage/geometry/polyhedron/base.py

@@ -4120,10 +4120,9 @@ def stack(self, face, position=None):
 
     def wedge(self, face, width=1):
         r"""
-        Return the wedge over a ``face`` of ``self``. ``self`` must be a
-        polytope and ``width`` must be nonzero.
+        Return the wedge over a ``face`` of the polytope ``self``.
 
-        The wedge over a face `F` of a polytope `P` with width `w \not\eq 0`
+        The wedge over a face `F` of a polytope `P` with width `w \not= 0`
         is defined as:
 
         .. MATH::
@@ -4136,23 +4135,24 @@ def wedge(self, face, width=1):
 
         - ``face`` -- a PolyhedronFace of ``self``, the face which we take
           the wedge over
-        - ``width`` -- a nonzero number (default: ``1``), the width of the
-           resulting polytope
+        - ``width`` -- a nonzero number (default: ``1``), indicates how wide
+          the resulted wedge should be
 
         OUTPUT:
 
         A (bounded) Polyhedron object
 
         EXAMPLES::
 
-            sage: P = polytopes.regular_polygon(4)
-            sage: W1 = wedge(P, P.faces(1)[0]); W1
+            sage: P_4 = polytopes.regular_polygon(4)
+            sage: W1 = P_4.wedge(P_4.faces(1)[0]); W1
             A 3-dimensional polyhedron in AA^3 defined as the convex hull of 6 vertices
-            sage: W1.is_simple()
+            sage: triangular_prism = polytopes.regular_polygon(3).prism()
+            sage: W1.is_combinatorially_isomorphic(triangular_prism)
             True
 
             sage: Q = polytopes.hypersimplex(4,2)
-            sage: W2 = wedge(Q, Q.faces(2)[0]); W2
+            sage: W2 = Q.wedge(Q.faces(2)[0]); W2
             A 4-dimensional polyhedron in QQ^5 defined as the convex hull of 9 vertices
             sage: W2.vertices()
             (A vertex at (0, 1, 0, 1, 0),
@@ -4165,7 +4165,7 @@ def wedge(self, face, width=1):
              A vertex at (1, 0, 1, 0, -1),
              A vertex at (1, 1, 0, 0, 1))
 
-            sage: W3 = wedge(Q, Q.faces(1)[0]); W3
+            sage: W3 = Q.wedge(Q.faces(1)[0]); W3
             A 4-dimensional polyhedron in QQ^5 defined as the convex hull of 10 vertices
             sage: W3.vertices()
             (A vertex at (0, 1, 0, 1, 0),
@@ -4179,12 +4179,18 @@ def wedge(self, face, width=1):
              A vertex at (0, 1, 1, 0, -1),
              A vertex at (1, 1, 0, 0, -2))
 
+            sage: C_3_7 = polytopes.cyclic_polytope(3,7)
+            sage: P_6 = polytopes.regular_polygon(6)
+            sage: W4 = P_6.wedge(P_6.faces(1)[0])
+            sage: W4.is_combinatorially_isomorphic(C_3_7.polar())
+            True
+
         REFERENCES:
 
         For more information, see Chapter 15 of [HoDaCG17]_.
         """
         if not self.is_compact():
-            raise ValueError("polyhedron `self` must be a polytope")
+            raise ValueError("polyhedron 'self' must be a polytope")
 
         if width == 0:
             raise ValueError("the width should be nonzero")
@@ -4197,10 +4203,11 @@ def wedge(self, face, width=1):
         for facet in face.ambient_Hrepresentation():
             if facet.is_inequality():
                 F_Hrep = F_Hrep + facet.vector()
+        F_Hrep = list(F_Hrep)
 
-        L = Polyhedron(rays=[[1],[-1]])
+        L = Polyhedron(lines=[[1]])
         Q = self.product(L)
-        H = Polyhedron(ieqs=[list(F_Hrep) + [width], list(F_Hrep) + [-width]])
+        H = Polyhedron(ieqs=[F_Hrep + [width], F_Hrep + [-width]])
         return Q.intersection(H)
 
     def lawrence_extension(self, v):