Polyhedron and Polytope (=compact Polyhedron) implies convex. For example:

sage: lp = LatticePolytope(matrix([[-1,-1], [-1,0], [0,0], [1,0], 
[1,-1]]).transpose())
sage: lp.points()
[-1 -1  1  1  0  0]
[-1  0  0 -1 -1  0]
sage: lp.vertices()
[-1 -1  1  1]
[-1  0  0 -1]

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