fix small dimensional cases

src/sage/geometry/polyhedron/base.py

@@ -3170,6 +3170,17 @@ def is_pyramid(self, certificate=False):
             sage: Q = polytopes.octahedron()
             sage: Q.is_pyramid()
             False
+
+        For the `0`-dimensional polyhedron, the output is ``True``,
+        but it cannot be constructed as a pyramid over the empty polyhedron::
+
+            sage: P = Polyhedron([[0]])
+            sage: P.is_pyramid()
+            True
+            sage: Polyhedron().pyramid()
+            Traceback (most recent call last):
+            ...
+            ZeroDivisionError: rational division by zero
         """
         if not self.is_compact():
             raise ValueError("polyhedron has to be compact")

src/sage/geometry/polyhedron/combinatorial_polyhedron/base.pyx

@@ -410,9 +410,15 @@ cdef class CombinatorialPolyhedron(SageObject):
             # one can give an Integer as Input.
             if data < -1:
                 ValueError("any polyhedron must have dimension at least -1")
-            self._n_facets = 0
             self._dimension = data
 
+            if self._dimension == 0:
+                self._n_facets = 1
+                self._n_Vrepresentation = 1
+            else:
+                self._n_facets = 0
+                self._n_Vrepresentation = 0
+
             # Initializing the facets in their Bit-representation.
             self._bitrep_facets = facets_tuple_to_bit_repr_of_facets((), 0)
 
@@ -1831,10 +1837,31 @@ cdef class CombinatorialPolyhedron(SageObject):
             Traceback (most recent call last):
             ...
             ValueError: polyhedron has to be compact
+
+        TESTS::
+
+            sage: CombinatorialPolyhedron(-1).is_pyramid()
+            False
+            sage: CombinatorialPolyhedron(-1).is_pyramid(True)
+            (False, None)
+            sage: CombinatorialPolyhedron(0).is_pyramid()
+            True
+            sage: CombinatorialPolyhedron(0).is_pyramid(True)
+            (True, 0)
         """
         if not self.is_bounded():
             raise ValueError("polyhedron has to be compact")
 
+        if self.dim() == -1:
+            if certificate:
+                return (False, None)
+            return False
+
+        if self.dim() == 0:
+            if certificate:
+                return (True, self.Vrepresentation()[0])
+            return True
+
         # Find a vertex that is incident to all elements in Hrepresentation but one.
         vertex_iter = self._face_iter(True, 0)
         n_facets = self.n_facets()