The loop

[Genady]

I've prepared a simple toy:

It consists of a pencil and a string that goes through a hole in the pencil and makes a loop. The ends of the string are glued together. 

The loop is shorter than the long end of the pencil:

so, it can't be moved over it.

Then, I insert the pencil through the buttonhole like this:

This is how it looks from the other side:

I can separate them again and repeat without cutting, breaking, untying, etc.

Can you figure it out?

I can take more pictures, from different angles, if you need. There are no hidden cuts or anything like it. You can make it yourself.

 

 

[Genady]

This is what happens if the pencil is pulled to the right:

and to the left:

How to get it out?

[Genady]

Reminder:

Spoiler

We live in a three-dimensional space.

 

[TheVat]

Spoiler

When you pulled to the left, you essentially made a knot.  To untie, you don't stretch the string, but rather stretch the fabric in three-space, as you reverse the original knot.  

 

[Genady]

Good! +1

And,

Spoiler

it can be easily solved when you pull to the right. Do you see it?

 

[Genady]

Spoiler

Except for a different parts orientation, taking the pencil off the buttonhole is not different from unbuckling a belt: