Hexagon shaped pieces elevator

Thanks for the answers, yes, they have a smooth surface so I might be using some 3d printer belt for the adhesion... Do you think using some pointy things would be better??

Talking about the gripping method, I've tested using a parallel grip with a Nema 17 and a lead screw from a 3d printer, I need to make an aligment mechanism but overall seems the way to go, the problem is that the sticks tends to bend at the end due to the force applied by the motor. Which encompassing nechanism do you mean? like making the grip with a hexagon shape?