Polyduranium is a material. Named for its relation to duranium, this substance was used by several states and races, mainly for defense.
In the year 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)