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I’ll show how to derive a formula for the Ehrhart polynomials for the type-$B$ generalized permutohedra, which offer a more concise alternative to the recent formula obtained by Eur, Fink, Larson, and Spink from their study of delta-matroids.  My approach utilized some of the techniques and tools introduced around 20 years ago by Postnikov from his study of generalized type-$A$ permutohedra, a family of polytopes that interconnects with many mathematical concepts such as matroids, graphs, and Weyl groups.