What are some examples of 2-polytope/3-polytope that are not simple?

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I've learned lots of stuffs in class about how to identify a simple polytope. But I've never seen a counter-example.

We use the following definition of simple polytope:

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Just take the dual of a non-simplicial polytope. For example, a cube's dual is an octahedron, which has 4 edges per vertex, not 3.