> I presume you can enumerate vertices and facets, 
>

Unsure on how easy it will be to do this for my use case.
 

> or remove redundant inequalities in a more direct way.
>

On a case-by-case basis, in principle, yes, this is the approach taken in 
the particular literature I'm looking at.  However, what I really want is 
the Ehrhart quasi-polynomials for these things, and it would be "best" to 
automate it completely from the original inequalities, which take a very 
predictable form.   Maybe it will be easiest to use non-strict 
inequalities, and then subtract off (as Matthias implies) the 
lower-dimensional equalities.  Thanks!

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