One tessellation where the verso looks really surprising.
It is possible to puff any of the hexagons, just not two adjacent ones.
One way to make this tessellation is to first start with a grid of everlapping twisted hexagons (2 crowns on the rector but only one on the verso), and then to transform every corner with triangle twists. I found that the easiest way to make the initial hexagonal tessellation is to make them row after row: in this way, during folding, the unfolded part of the paper alternates between two sets of parallel creases.