Tetrominoes cilinder

Edo Timmermans

You can find many
beautiful things on Edo his Youtube channel:

https://www.youtube.com/user/EdoTimmermans?feature=mhee

The tetrominoset is made with ningboballs that
you can buy at

http://www.ningboballs.eu/en/

You get a set of tetrominoes

With this set you can make the base form in 8 different ways.

Below you can see how this is possible.

Solution 1 and 2 form slightly different cilinder.

Solution 3A and 3B form the same cilinder.

Solution 4A and 4B form the same cilinder.

Solution 5 and 6 form slightly different cilinder.

Solutions 1,2,3,4,5 and 6 all fit in the base shape that forms the cilinder.

Solution 7 is the only solution that can not fit in this base shape and
still forms the same tube.

Can you find it?

Martin Grider made a video with the following
solution

We explain why this solution is not new: it fits in the base shape.

Helmut Postl sent us the solution and the following beautiful statement: *
"An interesting fact is that there are different cylinders as well, but none
of those can be built by the tetrominoes. The actual cylinder has height h=4
and circumference c=5. In principle, you can build cylinders with h*c=20,
that is (h,c) = (1,20), (2,10), (4,5), (5,4), (10,2) and (20,1). Since the
tetrominoes have odd checkerboard parity, the circumference must be odd.
This leaves (4,5) and (20,1), where the latter of course cannot be built by
the tetrominoes."
*The following picture may help to understand what Helmut means