Baseball (object)
A baseball was a spherical object, used in the game it was named for. Measuring approximately 0.22 meters in circumference, and 140 grams in weight, it was made of a lightweight core with a leather outer, stitched together by 108 stitches of red cotton.

Sisko's baseball 

In 2369, Benjamin Sisko received a baseball from an alien impersonating legendary baseball player Buck Bokai. He kept it on a stand in his office on Deep Space 9 and often tossed it between his hands during tense moments. He had previously kept a baseball with glove in his quarters. ()

In 2371, when Deep Space 9 was in the throes of a Cardassian counter-insurgency program, Gul Dukat briefly took over the office and tossed the baseball to the floor. ()

During the initial phase of the Dominion War, after the Dominion temporarily gained control of Deep Space 9, the baseball was left behind, serving as a reminder to Dukat, who had taken command of the station, that Sisko intended to return. () Sisko was given the ball back by Dukat following the latter's descent into madness, and the recapture of the station by Starfleet in Operation Return. ()

In an alternate timeline Jake Sisko kept his father's baseball in his house in Louisiana after his father's disappearance. ()

In 2374, following the sealing of the Bajoran wormhole by the Pah-wraiths, Sisko returned to Earth on leave. Kira Nerys noted that he took the baseball with him – a sign that Sisko was not sure that he would be returning. ()

The ball also helped Sisko locate the Orb of the Emissary on the planet  three months later. In a vision sent to him by the Prophets, the ball rested at the location where Sisko was digging. When Ezri Dax took the ball from him on the surface, and threw it away, Sisko realized that the Orb was located where it fell. ()

Sisko was given another baseball shortly thereafter, signed by the members of his senior staff in the Niners baseball team, after their game against the Logicians in 2375. ()

The baseball marked a symbolic passing of power by the end of that year – following Sisko's ascension to be with the Prophets, and Kira Nerys's promotion to station commander at the close of 2375, she picked up the ball for the first time. However, the fact that Sisko left the baseball behind also was likely a sign that Sisko would return someday. ()

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