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Three-Edged was a huge sword carried by Jillian during the reign of King Banhammer of Faq, prior to its fall. It is strongly implied that its pommel is the sword's "third edge" in that it serves as her sex toy.IPTSF Text 37
It's quite possible that it's the same sword that she's still carrying.
Real World References
Three-Edged is a reference to a quote from J. Michael Straczynski: "Understanding is a three-edged sword. Your side, my side, and the truth."