# Revision history [back]

### Is this polar polytope correct?

I have a polytope

sage: P = Polyhedron([
....: [-1, -1, -1, -1, -1],
....: [-1, -1, -1, -1, 6],
....: [-1, -1, -1, 6, -1],
....: [-1, -1, 6, -1, -1],
....: [-1, 6, -1, -1, -1],
....: [5/2, -1, -1, -1, -1]
....: ])


The polar can be constructed manually with

sage: Pd = Polyhedron(ieqs=[vector([1]+v)for v in P.vertices_list()])
sage: Pd.vertices()
(A vertex at (1, 0, 0, 0, 0),
A vertex at (0, 1, 0, 0, 0),
A vertex at (-2, -1, -1, -1, -1),
A vertex at (0, 0, 0, 0, 1),
A vertex at (0, 0, 0, 1, 0),
A vertex at (0, 0, 1, 0, 0))


This yields a result different from P.polar()

sage: P.polar().vertices()
(A vertex at (12/7, 6/7, 6/7, 6/7, 6/7),
A vertex at (0, 0, 0, 0, -6/7),
A vertex at (-12/7, 0, 0, 0, 0),
A vertex at (0, 0, 0, -6/7, 0),
A vertex at (0, -6/7, 0, 0, 0),
A vertex at (0, 0, -6/7, 0, 0))


Why am I getting different results? Is this a bug?

### Is this polar polytope correct?

I have a polytope

sage: P = Polyhedron([
....: [-1, -1, -1, -1, -1],
....: [-1, -1, -1, -1, 6],
....: [-1, -1, -1, 6, -1],
....: [-1, -1, 6, -1, -1],
....: [-1, 6, -1, -1, -1],
....: [5/2, -1, -1, -1, -1]
....: ])


The polar can be constructed manually with

sage: Pd = Polyhedron(ieqs=[vector([1]+v)for v in P.vertices_list()])
sage: Pd.vertices()
(A vertex at (1, 0, 0, 0, 0),
A vertex at (0, 1, 0, 0, 0),
A vertex at (-2, -1, -1, -1, -1),
A vertex at (0, 0, 0, 0, 1),
A vertex at (0, 0, 0, 1, 0),
A vertex at (0, 0, 1, 0, 0))


This yields a result different from P.polar()

sage: P.polar().vertices()
(A vertex at (12/7, 6/7, 6/7, 6/7, 6/7),
A vertex at (0, 0, 0, 0, -6/7),
A vertex at (-12/7, 0, 0, 0, 0),
A vertex at (0, 0, 0, -6/7, 0),
A vertex at (0, -6/7, 0, 0, 0),
A vertex at (0, 0, -6/7, 0, 0))


Why am I getting different results? Is this a bug?