This is a Klein Bag:
It is related to the non-orientable Klein Bottle, but I compromise a bit to make it embeddable in 3-dimensional space.
I made it from an old sock. I cut loose the ankle-tube from the foot of the sock, pushed the ankle-tube through a ring, folded the tube over, and sewed three of the four edges together.
To open it up, first push the ring down past the free edge:
Then pull the free edge up and over. This opens the bag.
For more than 20 years I have carried my change in klein bags.