Polyduranium is a material used by several states and races, mainly for defense.
In 2153, polyduranium was encountered by Enterprise in the doors of a Delphic Expanse sphere and in the hull of an Osaarian ship. (ENT episode: "Anomaly")
The hull plating of the USS Defiant included a mix of polyduranium, kelindide, rodinium and toranium. (ST reference: Star Trek: Deep Space Nine Technical Manual)
Polyduranium was also used in a bulkhead on the bridge of the Defiant. In 2371, Ornithar expressed an interest in it but he believed it had no real value. (DS9 episode: "The Search")
Polyduranium is also used in the casing of Klingon bat'leths. (ST reference: Star Trek: Deep Space Nine Technical Manual)