Non $0,\pm 1$ integer coefficient polytopes with integral extreme points

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Suppose we have a linear system

$$Ax\leq b\quad \text{where}\quad A\in \mathbb{Z}^{m\times n},b\in \mathbb{Z}^m.$$

In integer programming literature, we usually have that $A$ has only $\{0,\pm 1\}$ entries, including totally unimodular matrices.

Suppose instead $A$ is integer-valued in general, is there any well-known class of polytopes that has integer-valued extreme points in the literature?

Thanks.