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Aftermarket winter rims: lug nut seat angle?

I've been shopping for some winter rims, factory rims from Tesla supposedly won't be available until the first week of November which cuts it pretty close for my climate. I was at a tire store on the weekend pricing out options and was told that I would have to buy a whole new set of lug nuts because the lug nut seat angle for aftermarket rims is different than Tesla's. This sounded like a bit of a scam to get me to spend another $75 in their store, is there any truth to it? I couldn't find any detailed specs on the factory lug nuts, I used a crappy plastic protractor from an old geometry set I had at home to measure the lug nut seat and it appears that the seat angle is around 60° - by no means was that precise.

I know that lug seats can have different shapes :

Performance Alloys.com®“ Wheel Nuts & Wheel Bolts - Long Wheel Nuts: The Alloy Wheel Experts

but I've not heard of different seat angles. Having different angles seems like an unnecessary complication when ordering rims.
 
Interesting. So would the Tesla nuts be the 'bulge acorn' style?

Lug Nut Info

I'm just curious what they'd be called so that I can try and track down a set of rims that'd work with the stock nuts. It'll definitely be tricky with all the specs (offset, centrebore, lug spacing...) that already need to be met.

Lots of manufacturers are now using acorn style lugs. They have a curved seat with lots of surface area given their size. Unfortunately, you will have no luck finding acorn seat aftermarket wheels. They use tapered tuner lugs practically as a rule, so you should probably just accept that you'll be buying lugs as well.
 
I guess I've had my terminology mixed up all these years. Tapered means in the shape of a cone, which makes sense. I've never associated acorn with tapered lug nuts before, though. I've only associated with ball/rounded seat lugs, because it gives them the appearance of an acorn which are rounded at the bottom. I'd edit my previous post so that it doesn't confuse anyone, but it looks like I can't :(.

To accurately modify my post:
Lots of manufacturers are now using ball/rounded lugs. They have a curved seat with lots of surface area given their size. Unfortunately, you will have no luck finding ball seat aftermarket wheels. They use tapered tuner lugs practically as a rule, so you should probably just accept that you'll be buying lugs as well.
 

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