The question got resolved and this post of mine is a bit tangential. Hence, I have chosen to delete it.
Thanks.
There is no such term "enough" in polymake's philosophy. Either the property is complete and correct or it does not exist at all. So in your case if the problem turns out to be intractably large, it will just run forever or stop due to lack of memory, but it will never give you a "partially true" answer. This is the fundamental difference to commercial software aimed at solving a business problem, where a slightly suboptimal solution obtained in reasonable time is accepted for obvious reasons.how does polymake ensure that the LATTICE_POINTS enumerated are exhaustive enough?