Advantages: maybe smaller fins (although that didn't pan out for me), maybe easier to pack chutes in the tube, different from everyone else's rockets.
Disadvantages: Nearly everything else. You have to lay up your own tube, figure out couplers, figure out a nose cone, etc. etc. There's so much stuff that's built around standard sizes of round rockets that you don't realize how much you'll have to re-do.
See my build thread here:
https://www.rocketryforum.com/showt...don-A-square-rocket-that-doesn-t-quite-fit-in
I disagree. At least for low power and mid power. Can't speak for high power
Nose cones? Easy and CHEAP! Can readily be folded out of card stock origami style to fit any size you want the make.
Body tubes? Can be folded out of poster board, may have to double it up.
Centering rings? Well, they would be squares. Again at least for low power can be cut out of foam board easily. I have an 18 mm drill mounted hole saw which, with a touch of sanding will easily and securely fit BT-20 for an 18 mm engine motor mount. A 24 mm works to fit a BT-50 for 24 mm mounts. Drill your hole first, then center your square cut around the hole and cut out with an exact knife and a metal ruler.
Fins? Don't understand how you think you can use smaller fins, if anything due to increased drag from the origami geometrically angled cone will move CP a bit forward and you will need more fin area. But attachment? Think literally outside the box. Stick the fins flat along the side sticking out parallel to the sides of the rocket. They won't look symmetrical but your alignment will be automatically perfect and they will work fine, and look cool.
Performance? Okay, definitely will take a hit, but you aren't building for altitude, you are building for the cool factor (and its cheap, for simple LPR rockets I have read that the most expensive part of the kit is usually the nose cone.) As I said, for card stock costs you next to nothing. Can't say that for a standard o give 1, 2, 3, or 4 inch cone.
By the way, why stop at square? Think triangle, pentagon, hexagon.
Think outside the circle!