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space hopper

n. A toy; consisting of an large inflated rubber ball, upon which one bounces.

Wikipedia
Space hopper

A space hopper (also known as a moon hopper, skippyball, kangaroo ball, bouncer, hippity hop, hoppity hop, sit and bounce, or hop ball) is a rubber ball (similar to an exercise ball) with handles which allow one to sit on it without falling off. The user can hop around on the toy, using the elastic properties of the ball to move forward.

The term "space hopper" is more common in the UK; the toy is less familiar in the United States, and may be known as a "hoppity hop", "hippity hop" or a "sit n bounce". A similar toy popular in the U.S. in the 1980s was the pogo ball, which has a hard plastic ring encircling the ball instead of a handle.