I agree with tigerstrat, Jerry had the Les Paul with the SG shape. I think those were only '61s but I could be wrong. I have a '59 Les Paul special which is kinda like an SG, Dbl Cut slab mahogony body and two pickups, I think the necks similar as well - on mine anyway because the neck is a replacement.
SGs are the first guitar I took notice of, I saw pictures of Jerry and Zappa as well as Santana, Allman, Alice Cooper's guitarist, Clapton, Harrison, Robbie Krieger, Townsend; on album covers, at Woodstock, in the 'Live at Leeds' package etc. It was definately 'the' guitar at the time.