Cardboard-i-copter wasn't a project so much as a fortuitous discovery.
A few years ago my uncle gifted me this quadcopter: https://www.amazon.com/gp/product/9269802574/
Unfortunately I couldn't get it to fly. It mostly chaotically bounced around the room. Friends with many more quadcopter flying hours than I all failed to get it to fly.
One night while hanging around the main Sector67 table, I pulled the roll cage off. Still no dice. So I disassembled it entirely, and then as a joke, taped the electronics and motors to cardboard.
Nothing about this configuration was rigid or carefully measured or square. It seemed to self-right the motors so long as they were more than 45 degrees off the plane of the cardboard. It was pretty easy to fly. It was incredibly easy to repair after a crash.
Eventually it developed an issue with the control system that sometimes caused it to go full throttle and unresponsive. Those props are kind of painful to fingers and I was sick of chasing it down and fighting it to get the battery unplugged.
It would be fun to explore cardboard-i-copters more one day, formally (the physics of it), and informally (building a bunch of designs). If you have some cheap mini quadcopters or quadcopter parts lying around, try it and let me know how it goes.