@Rouben Rostamian  Wow, very nice! I can confirm your conclusion by empirical verification (failing to fit the rolled carpet in the box without deforming any of them). Surprising that only 8.4 mm is gained by inclining it from the bottom of the box. As a note, I ended up folding the carpet 2x2! Anyway, thanks for the interesting solution and documentation/comments in the maple sheet.