Have you ever seen a paper balloon? The Japanese toy called kamifusen has been around for over 100 years. Japanese mathematician Tadashi Tokieda blows one up, but that's not the only way you can make your kamifusen round. The other way is srprising.
Rocket scientist Ichiro Fukumori wrote about the properties of kamifusen.
Part of the kamifusen’s genius is the paper from which it is made. The paper is not only lightweight and relatively impermeable to air, but it also has a degree of plasticity that allows it to deform easily and retain its resulting shape. Because of those properties, the kamifusen inflates to a volume commensurate with its air content and maintains that volume until additional air is added. As a result, a squashed kamifusen can accumulate air and eventually inflate to its full size from repeated bouncing, even though the net pumping from a single bounce may be small. A balloon made of plastic, rubber, or any other material that does not share the key properties of kamifusen paper would not inflate as the Japanese balloon does.