theres a webiste you can go to that gives all the info on U2 equipment:
http://www.u2sound.de/
go to the edge and scroll down to the gibson w/ discotheque finish
There is also an interesting story about the black/black strat:
Fender Stratocaster 1979, black, black pickguard,
The Edges? guitar from the tour highlighting the "Joshua Tree" album. It was also used during the filming of Rattle and Hum. Autographed twice by Bono. 1979 Fender Stratocaster serial #s 916792. What is special about the guitar is the story behind it. Sometime during the late 1980?s, The Edge was asked to autograph a guitar to be presented to The Hard Rock Caf?. The Edge agreed to do so. One day, in 1988, New York, The Edge decided to go to The Hard Rock Caf?. He went to the front along with Bono and a guitar. There was a long line; and a doorman. The doorman told The Edge he would have to stand in line with everyone else. Edge replied," I?m The Edge. I?d like to get in." The doorman stood his ground. "You?ll stand in line like everybody else," he said. Rebuked, The Edge started to leave the caf?. Bono grabbed the guitar and said, " I?ll sign it." He did so on the spot, with a red felt pen, and the autograph, now dimmed by time, reads "Bono, 88". When the guitar was presented to the Hard Rock Caf?, the caf?s representative declined it on the ground that it was not signed by the Edge! Black body shows scratches on back of the guitar from the Edge?s belt buckle. In 1993 the guitar was again presented to Bono to resign and he laughed when he was reminded of the story. Bono resigned the guitar, again the Edge still pissed off refused to sign. Valued at $12.000,00. I personally think, that this is a rip-off! This guitar may be identical to Edge's old main working horse! You can see the guitar in the video to "Where the streets have no name"
It's a really great site. Wish it had pics!