I have a Polaris 570 thinking of getting 27x10x12 silverback mud tires what size rims can I buy for those tires

 

It already has 12" rims why buy another set of rims? The last number is the rim size so you need 12" rims like it already has.

 

one rim has a dent in it and I wanted a different style rim when I know I need a 12 but wasn't sure if that's the only dimension I have to worry about with these tires

 

OK, use this chart it explains everything you have to make sure the "Off-Set" is also correct. ATV Tire and Wheel Application Chart : ATV Tires Free Shipping : ATV Wheels : Mud-Throwers.com

If your ATV is not on the chart you can measure your Offset and rim width on your own just to be safe. Your bolt pattern is 4/156

The pic bellow is a 7" wide rim with a 4+3 Offset. To give you the idea.

 

Okay thanks

 

If you're buying wheels from a website or dealer, they will make sure you get wheels that fit your machine. But yes, its good to know your bolt pattern to know if wheels from another machine will fit your ride. Sometimes a particular bolt pattern is shared by many different models. Like a Grizzly 660 for instance has the same bolt pattern as I believe a King Quad 700, Brute Force 750 and a Honda Rincon. Possibly even more. A chart like TLC posted is useful in showing if your machine shares a bolt pattern and offset with another machine in case you see a good deal on a used set of wheels and tires that may have been on another quad but will fit yours.