Originally posted by anstratdubh1979:[..]
Here's the answers you requested:
"Desire" and "Van Diemen's Land" in the Rattle and Hum (film) are a 1962-ish stereo Gretsch White Falcon.
"Desire" (Rattle and Hum) video:
[YouTube Video]
"Van Diemen's Land" (Rattle and Hum) video:
[YouTube Video]
That said, Dallas has said that the album version of "Desire" was the 1975 Les Paul Custom (that was auctioned off at the Music Rising Icons of Music auction in 2007).
Also, during the Lovetown tour, The Edge was using a Stratocaster for (at least some if not all) live performances of "Van Diemen's Land".
Van Diemen's Land (Lovetown tour)
[YouTube Video]
As for the White Falcon, I've yet to see The Edge use it for anything in a live concert setting, other than for
"Ultraviolet (Light My Way)", during the Zoo TV tour was played on his 1976 Gibson Ltd. Ed. Explorer.
"Ultraviolet" Washington DC Zoo TV video.
[YouTube Video]
For the U2:360 tour, he's switched to a Fernandes RetroRocket. Reason? Decided to rearrange the solo and use the sustainer pickup of the RetroRocket.
"Ultraviolet" U2:360 video
[YouTube Video]
Wow.. Did you look all that up or do you just know?

