1. Gibson EDS-1275
No we're not kidding, we really think that the Gibson EDS-1275 is the coolest obscure Gibson. It's aesthetically quite hideous, which is a standard litmus test for a collectable guitar, and it was famously used by Jimmy Page, which gives it an instant seal of approval, even if it was huge and unwieldily.
You can now pretty much only get away with using it ironically or for a joke, and that's why it's the coolest, because the excess of the two necks and the gold hardware has come to symbolise all that is wrong with rock and roll, and it has become the most obscure Gibson model thought being (wrongfully) shame out of the spotlight.
If you turned up on stage with one of these at a local bar, you'd be laughed off the stag before you even struck a chord, and that's a tragedy for any guitar. We understand the EDS-1275's pain, and we want to make it better by letting it know that actually, it's pretty cool.
The idea of a 12-string guitar and a 6-guitar fused together is pure genius, if a little insane, and allows for all sorts of maniacal playing.
Don't deny it, you secretly think this guitar is cool, you're just too scared that people will laugh at you if you own up to it!