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The current difference between the base ring QQ and ZZ for polyhedron objects in Sage is not quite big nor quite well defined...

A polytope (a compact polyhedron) may have all vertices with integer coordinates, so that it could be called a "Lattice polytope", but its H-representation may still contain rational numbers. Of course, it is possible to multiply all coefficients in the H-representation by a certain integer factor to get an integral H-representation, but this is not automatically done in Sage.

The tickets Add .change_ring() method for polyhedra and Add .change_backend() method for polyhedra will then make it possible to apply the desired changes on the base ring and backend, if possible.

The current difference between the base ring QQ QQ and ZZ ZZ for polyhedron objects in Sage is not quite big nor quite well defined...

A polytope (a compact polyhedron) may have all vertices with integer coordinates, so that it could be called a "Lattice polytope", but its H-representation H-representation may still contain rational numbers. Of course, it is possible to multiply all coefficients in the H-representation H-representation by a certain integer factor to get an integral H-representation, H-representation, but this is not automatically done in Sage.

The tickets Add .change_ring() method for polyhedra and Add .change_backend() method for polyhedra will then make it possible to apply the desired changes on the base ring and backend, if possible.