I just purchased two 36mm threaded headset tools, thinking both the locknut and the race/nut were 8-sided 36mm. It turns out the locknut was 6-sided. Because of the way the tool is designed to cup an 8-sided nut on 6 sides, it can not be used on the locknut nor can it be used on the race/nut (since it would need to slide onto and over the locknut). Are 6-sided locknuts the standard?

Just to be clear, the tool is similar to this (where it cups the nut). The mouth/opening of the wrench is not wide enough to clear the spacers under the locknut. So, in theory, it seems the tool would have to slide over the locknut, over the spacers, and then onto the race/nut.

EDIT: Actually, I just realized I'm even more confused. The locknut appears to have a flange at it's base, wider than the mating surface for the wrench. So, even if it was eight-sided , the wrench could still not slide down to the race/nut. I'm seriously confused.

That's a locknut wrench, designed thicker than the standard headset wrench to address fact that locknuts are tightened down and thinner wrenches are not substantial enough to loosen them. I have never had a problem using standard thin headset wrenches on locknuts. You can use your wrench on locknut and perhaps get yourself something like attached to deal with the top cap.

Get a 12" crescent wrench for the locknut

+1 As long as you have a thin headset wrench to hold the top race in place, the locknut can be tightened with nearly any suitable size wrench as thickness isn't a problem.

That's the problem: I can't get the thin wrench I ordered down to the race, because it has those additional lips (to grab 2 additional nut sides). I have a huge crescent wrench for the locknut.

For removing it, a large crescent wrench is all you need.

For installing and adjusting a proper headset wrench is needed (alternatives to that are some locking pliers on the top race body, but that likes to marr the finnish, and may distort out of round if clamped too hard, better avoid this)

You need a different wrench. Check out the ones from Park Tools, they make a very thin but strong wrench in 36mm that is designed to specifically fit in the small space below the locknut.

Your thought pattern was correct when you bought the wrench you obtained but it is not quite suitable for your needs. You should check into returning it our keep it use on the locknut...but you will need a thinner wrench like I recommend above for the adjustable cup.

Good luck.
-j

Thats because its a locknut specific wrench.

I got really lucky. I went to Home Depot and they had a 10" crescent wrench that is EXACTLY 36.2mm at full extension. The package actually said "Max 35mm", but I asked the employee if we could open and measure. It is an absolute perfect fit for the race - and the beauty is that it won't slip any further. And another bonus: I can use this wrench for all kinds of other jobs.

Park headset wrench for the adjustable nut.

Check and see if you have a crescent that opens large enough to use on the locknut. If not, get one, or get a second headset wrench of the appropriate size.

Rock 2 wrenches like this.

If you haven't already, then in order to ensure you order the right size wrench(es), it's probably best to measure the exact sizes of the wrench flats with a caliper (which is a useful tool for bikes anyway).