Mobius strip model

Laser cut the part. Make sure the notches are completely cut through and that the piece is flexible.

If you decide to scale it down, I wouldn't recommend going below 60% of original size with 3mm basswood plywood.

Slowly bend the pieces as shown in the pictures above. 

To make things easier, you should mark one side on one end and the other side on the other end. Once the part is joined, the marks should be facing to the same side.

It is easy to connect the ends together the wrong way so adding the marks will help a lot. You can use small piece of tape.

Glue the ends together, making sure you apply enough glue so the part won't fall apart. I found it easiest to use clamps with some brackets to align the ends. Make sure you don't glue the brackets to the parts. I usually use masking tape over the glued part for this as it is easy to remove.

You can also use superglue and simply hold the pieces together until it cures enough.