And LatticePolytope has various compile-time limits like the maximal number 
of dimension and vertices before you hit a C assertion. Whereas Polyhedron 
has no limits within your CPU/Memory bounds. 

Starting with Sage-5.6 the Polyhedron class also supports the base ring ZZ. 
In the long run I'm envisioning this as the replacement for the current 
lattice polytope class. There is also a Cython PPL lattice polytope class 
at #12553 if you need something very fast.

On Saturday, December 29, 2012 2:03:48 PM UTC, Johhannes wrote:
>
> p.vertices() gives a list of lists, i.e. a list of vertices 
>

Not any more, with sage-5.6 it'll return a list of vertex objects (that 
behave like lists):

sage: polytopes.n_cube(3).vertices()
(A vertex at (-1, -1, -1), A vertex at (-1, -1, 1), A vertex at (-1, 1, 
-1), A vertex at (-1, 1, 1), A vertex at (1, -1, -1), A vertex at (1, -1, 
1), A vertex at (1, 1, -1), A vertex at (1, 1, 1))

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