Georgia-Pacific SofPull 56509 Smoke Twin High-Capacity Centerpull Bathroom Tissue Dispenser

Are the replacement rolls specific to a certain brand or do any large dispenser toilet paper rolls work

I have many rolls that are 3#1/2"wide, 10" diameter. The cores are 2&1/4"inside, 2&1/2"outside. Will they work in this dispenser?

what are the dimensions?