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you are indeed correct, the posts are different between rotaries (circular) and random orbitals. Two choices really , one is to exchange backing plate to correct model or second is to use the adapter that I forwarded in earlier post. (tighten well)
Good way to look at the backing plates is the Rotary is a female and the DA is a male!
If you are using a Porter Cable you will need the male DA backing plate like this one.
Designer Imagines A Corvette That Looks More Like a Corvette Than the Corvette
Slideshow: A Jaguar designer's personal project imagines what a modern front-engined Corvette might look like if Chevrolet revisited the golden age of the Stingray.