Couldn't you get a similar effect of you cut a left hand thread over a right hand thread?
Well, in order to get the diamonds running lengthwise like a knurling tool, wouldn't you need a multi-start thread? Both in Left and Right-hand? Sounds like a lot of work to me...but then again, I haven't had to attempt a multi-start thread yet!!
Of course, there's nothing to say that the knurls couldn't run cross-wise, then it shouldn't be too hard to figure out a pitch that looks nice. Say 10-20 TPI, depending on what you want...Hmmm, on second thought, the knurls still wouldn't look right - they'd be veeeeeery long diamonds, since each diamond would basically wrap all the way around the diameter.
You'd probably still need a multi-start thread, just not as many - depends on diameter.
Now you've got me wondering if I can get out of "kids duty" tonight and escape to the shop for an hour to try this out...
Andrew