This is a fairly simple model to fold, assemble and is fun to play with. For materials I'd suggest something a bit thicker than printer paper, some thin color paper worked like a charm. I made the printer paper model first but it seemed to twist quite badly and didn't return to it's original shape.
This model is made of 2 different units which are almost identical, only difference is that the end pieces have less folds on one side. Here's how you fold them (I decided to use some of my home made tissue foil since it's easier to see steps with and I wanted to try it out):
You start with a 1:2 rectangle
Fold in half
Unfold and fold towards the middle from both sides
Rotate 90*
Fold a corner up
Fold towards the corner
Rotate 180*
Fold along the diagonal
Unfold everything
Reassemble using existing creases(2 images to help)
Repeat on the other side(under the corner flap, raise if necessary)
Push the remaining corner under
Fold in half
Rotate 90*
Fold along the layer in the back
Fold bottom flap up
This is where the middle and end piece begin to differ, for the middle piece you repeat the last 2 steps in the back and for the end piece you simply fold the little corner in
This is the end piece with the corner up
And now the middle piece
Here's how they compare
The assembly is not that hard, to start you join 8 end pieces to form a ring. after that you just keep adding middle pieces till you're satisfied with the height. You'll need 8 pieces for the horizontal inner part and 8 for vertical, in short there are a lot of pieces but you can make it as big or small as you want.
In case someone is lost with some steps here is a video tutorial for the model where I learned it and decided to make it as tall as I could but gave up at a bit over 100 pieces. I wanted to add the assembly photos but it's much easier to explain with video but my previous origami-video setup was a nightmare.
And finally here's a gif of the tower in action
Hope you enjoyed my post, have a nice day :)