I am confused by polyhedral cell. I have read the article by Peric. It makes a good sense. However does it take a feature of geometry, similar dimension. If not, what is the point.

Polyhedral cells are basically a step up from tetrahedrals in that their generation is automatic and is grown from a surface triangulation, the point of them is that they are easier to generate than hex/trim meshes but have nearly comparible accuracy, are faster to converge, more accurate and less numerically diffusive than tetras

Thank you Ben. But I guess those cells in between polyhedral cells would be smaller in size so that would finally break the rule: change in cell size < 1.2?

There are generally no cells between polyhedral cells. In 99.9% of all cases, polyhedras are connected to other polyhedras.