Polyhedron_base._polymake_init_: Add work around for empty polytopes …

…with Polymake 3.0

src/sage/geometry/polyhedron/base.py

@@ -5453,9 +5453,18 @@ def _polymake_init_(self):
         """
         from sage.interfaces.polymake import polymake
         polymake_field = polymake(self.base_ring().fraction_field())
-        return polymake.new_object("Polytope<{}>".format(polymake_field),
-                                   FACETS=self.inequalities_list(),
-                                   AFFINE_HULL=self.equations_list(),
-                                   VERTICES=   [ [1] + v for v in self.vertices_list() ] \
-                                             + [ [0] + r for r in self.rays_list() ],
-                                   LINEALITY_SPACE=[ [0] + l for l in self.lines_list() ])
+        polymake_class = "Polytope<{}>".format(polymake_field)
+        if self.is_empty():
+            # Polymake 3.0 cannot enter an empty polyhedron using
+            # FACETS and AFFINE_HULL.  Use corresponding input properties instead.
+            # https://forum.polymake.org/viewtopic.php?f=8&t=545
+            return polymake.new_object(polymake_class,
+                                       INEQUALITIES=self.inequalities_list(),
+                                       EQUATIONS=self.equations_list())
+        else:
+            return polymake.new_object(polymake_class,
+                                       FACETS=self.inequalities_list(),
+                                       AFFINE_HULL=self.equations_list(),
+                                       VERTICES=   [ [1] + v for v in self.vertices_list() ] \
+                                                 + [ [0] + r for r in self.rays_list() ],
+                                       LINEALITY_SPACE=[ [0] + l for l in self.lines_list() ])