How high is your ceiling? Important, because subs work with room volume as opposed to distance-from, like your speakers.
For example, if you have 8' ceilings, you are almost at 5000'3, which the bassaholic rating here at AH would call Extreme! You would be looking at wanting at least 1, probably more, 13-15" subs... like the PB 3000 or 4000, Outlaw x-13, monolith 15", Hsu vtf3 or vtf15, or rythmik 15". Anything smaller is going to leave you wanting.
Now... if your room is open to other areas... those omni-directional LF waves are going to go anywhere and everywhere they please!
As far as anything from Polk... I'm afraid those dogs won't hunt. There are tricks to help you perhaps use less woofage in your space, but seriously... you should research a little before you buy.
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Read the Bassaholic room rating protocols here at AH, and you will see if you read any sub reviews here that they reference Large or Extreme rooms. Also read about setting up subs... especially multiple subs. It very well might come in handy and help you avoid making a poor decision!
As an example, in our greatroom, about 8000'3, I have a 10yr old dinky 10"sub from an old HTIB. Yes, I hear bass... but I don't feel it. If I turn up the volume, cabinet doors rattle, but it doesn't do much anything else. That's distortion from an undersized and underpowered sub being used in a room WAY to f'n big for it!
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In my 2000'3 space with my rig, I have 2 nice subs that will make my ears go numb if I turn them up to about 50%gain! I keep them around 1/4-1/3 gain, and have them trimmed down in the AVR too.
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I can turn them up and shake the house apart if I need, but am happy to have them perform well for me now and for a long time to come. I bought them for the greatroom, but the lady changed her mind. If I were using them out there, I would be saving for a third as we speak!
A friend here has a recommendation that I adopted because it is straight up truth: Buy the single best sub for your room that you can allow yourself to afford now, and immediately begin saving for a second one.
I would be glad, as would many here, to help you make sense of it all. Don't be afraid to ask.
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Please, if you do, let us know about complete room volume, and whether there are more areas that your room is open to.
Cheers!