My water diverter is screwed on to the outdoor faucet, but now it's stuck and it won't budge in either direction (black connector in images). It has four equidistant "notches" intended for gripping, but they actually make it more difficult to grip with a tool.
What I've tried so far:
turning by hand (with towel to avoid finger bruising)
"chisel" technique with screwdriver and hammer against one of the notches
tried to grip with wrench, but can't fit a round more than one notch
What tool or technique is best to get this unstuck?
Soak a rag in CLR™ and wrap it around the top of the black fitting.
This is one of several products designed to remove Calcium, Lime, and Rust, and just happens to be the brand I'm familiar with.
Soak it thoroughly so the liquid can drip down into the fitting, but, hopefully, not so much that it all drips off the rag onto the ground
This may help dissolve some of the mineral that's holding the fitting tight.
Try to loosen it about once an hour as the solvent soaks in. Eventually, you may dissolve enough to undo it by hand.
Soak a rag in a penetrating fluid (PB Blaster™ is my favorite for loosening old bolts on the car, others work, too).
Same notes as above
Get a bigger wrench.
A slip-jaw wrench or pipe wrench should open more than enough to grip across two of the flanges sticking out, giving you some leverage to twist.
There's a non-zero chance that the wrench will chew up the plastic enough that you may feel it's necessary to file/sand the plastic down so you don't hurt your fingers using it the next time.
Note: You could pour either of the fluids directly onto the fitting, but you end up with most of it dripping off. The rag should hold the majority of the fluid in place, allowing it to drip out into the fitting instead of just running off.
A big set of tongue and groove pliers (of which Channelock® is the USA brand many folks confuse with the type. Not an endorsement, pretty much like saying Band-Aid® is what lots of folks call any adhesive bandage.) So I'll just grab a picture from their website, and folks can chime in with whatever local brand is the default elsewhere in the world. Or if people actually call them tongue and groove pliers, for that matter. (Commenting that is explicitly encouraged!)