So I'm familiar with different polytopes where the number of facets is greater than the number of vertices and vice versa.
Examples include:
The n-dimensional cube, which in general as $2n$ codimension 1 faces and $2^n$ codimension n faces.
Then of course the dual of the cube which has $2n$ codimension n faces and $2n$ comdinesion 1 faces.
Now I'm curious however if there exists a class of shapes, where the codimension-k face $k \ne 1, n$ is minimal over all possible faces. In some sense if we assign a natural number to the total count of the faces of a particular codimension. Then need this list have it's smallest values at the ends? Or is it possible for the list to have its largest values near the middle?