Please help

If that is a tap with four grooves between the four sets of cutting teeth, there is a tool that consists of four spring steel fingers that slide into those grooves, then you turn that tool. It only works if the tap is broken off but not stuck tight.

The next plan of attack would be to weld a nut to it that you can put a socket on, or weld a steel rod that you can bend into a handle on the end.

Woops. Do I understand the tool is stuck in the socket? Sorry if I read that wrong. Put a punch into the square opening of the socket, hold it a few feet off the concrete floor, then let it drop straight down so the other end of the punch hits straight on the floor. Do that a couple of times and the stuck tool, bolt, or nut will come flying out and you can catch it in midair. Works much better than putting the socket in a vice and trying to tap the item out.

Doc I think he means that a tap is broke off in his spark plug threads

He has some kind of "extractor" that resembles a 4 sided castle nut, that I'm guessing slides down into the "Voids" of the broken tap.

Thus giving you a way to turn what's left of the tap, to remove it.

You might try re-explaining the situation---let me know if I'm tracking right.

The Medic

Read it several more times.I'm not tracking right. Sounds like your plan would work Doc, I might try a vise with something heavy plastic over the tap teeth as to salvage the tap. Then channel locks or a pipe wrench to tweak it a bit, to get it un-wedged from the socket teeth. The description of the tap threw me off.

For future reference, they do make 8 point sockets!

Still I am stumped with the "or weld a steel rod that you can bend into a handle on the end."

Sorry I was a hinder and not a help

The Medic

That first reply was when I was thinking the tap was stuck in the head. Spark plug holes are at an angle so holding a nut in place to weld it to the broken tap, (or bolt), is really hard. It's easier to hold a foot-long steel rod in place while you tack-weld it. A bolt would work better because it already has the head that you can hook a socket and ratchet to, but the sparks from welding makes that bolt hard to hold onto. A piece of re-bar works too. You can turn it with a vise grip. My comment about bending the end into a handle probably added to the confusion.