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An axe (or ax) was a multi-purpose tool consisting of a heavy and solid sharpened metal head attached to a helve. Axes were often also used as weapons in melee combat.
A Romulan miner from 2387 fought the alternate reality's Hikaru Sulu with an axe on the Narada's drill platform in 2258. (Star Trek)
In 2268, Ronald Tracey used an axe as a weapon as he fought against James T. Kirk on the planet Omega IV. (TOS: "The Omega Glory")
Decades later, in 2293, Kirk was trapped in the Nexus, and, when Jean-Luc Picard entered the Nexus in 2371, he found Kirk putting an axe to its most common use – chopping wood. (Star Trek Generations)
In 2367, Commander William T. Riker told the bridge crew a joke with a punchline about a headsman's axe. (TNG: "Data's Day")