OK, I'll be honest here. I haven't got one of these in my collection, even though I covet one. For the folks who've never seen one, that picture's of the CPU - no memory, no disks, no peripherals (well, OK, there's a paper tape reader/punch above the console and a DK-10 real-time clock behind the door under the console) - just the processor.
DEC's PDP-10, perhaps better known by the "DECsystem10" moniker, was based on an architecture utilising 36 bit words and an 18 bit (256 kw) address space. The entire -10 line was a direct descendant of the PDP-6 , first introduced in 1964 (of which only 23 were built); the basic instruction sets were identical.
The first of the PDP-10 line was the KA-10, introduced, just perhaps (I've heard rumours on both sides), as an engineering upgrade to the PDP-6 replacing said processor for alleged reliability problems. The KA-10 followed directly in the footsteps of the PDP-6 in that it was an asynchronous machine (i.e. not controlled by a central clock, but rather by "completion pulses" passed by hardware "subroutines"). The KI-10 would leave this mould and become a synchronous device (thereby beholden to exacting timing criteria, which were frequently a maintenance engineer's nightmare).
The KI-10 was Digital's ultimate (in my humble opinion) DECsystem-10 processor. It was fast, reliable, and elegant; unlike the later KL-10 and KS-10 models, the KI was a "hardware" (i.e. time-state) implementation rather than a microcode hack. (The KL-10, with its cache turned off, was actually slower than its grandmother, the KA-10.) In fact, the KI could frequently be driven as much as 20 percent faster than Digital's spec's allowed. I, personally, have seen KIs run with the 110 nanosecond clock set as low as 80 ns, and still be reliable.
As proof that I actually have been in the presence of these majestic machines, I offer this image, and apologies to Lynx users: (I'm slouching a lot and leaning on a DF-10 data channel):
If anyone reading this has knowledge of where I might find one of these machines, I'd appreciate an Email with details! My wife will most likely kill me for it, but I'm willing to take that chance.
For that matter, get hold of me just to reminisce about them... I've not seen one in better than a decade, and I miss them (The date code on the picture reads "86 10 22"; the photo was taken just before the -10s were returned to my first employer's home office). I, sadly, assume the individual here has long since been scrapped.
For those interested in the 36-bit heritage, I heartily recommend
Joe Smith's page