The pyramid shape (side view) is because it's easy to hook up to a single light Chimera/soft box frame. It's just a product of making the softbox larger than the light. Also any stray light gets reflected in the correct angle by the roughly 45 degree sides. You do see more rectangular profiles in soft boxes for multiple lights (often called a coffin box).

Ok I'm ditching the project for now. I made the whole frame out of lightweight wood, but it's just impractical and still heavy. Maybe a pvc frame would be easier to deal with? I could also just she'll out the $115 and get a 2'x3' 4 socket softbox on Amazon. That's sounding great right now.

@joethepro Sorry, I don't really have an example of a coffin box. It's not from web sites or books, it's just a thing we use sometimes on film sets for particular lighting needs. (They're often built on the spot from showcard, duvatyne, and grip equipment.)

All told, I'd recommend getting the real deal (used is fine). It will be far easier and faster to set up and safer as well. Because they are enclosed, softboxes hold more heat than open face lights and they can melt or catch fire if not made from the proper materials. It's not an item that I would DIY, FYI.