Why a box
Most of my work sits behind a login, and this is the exception. It is the same problem I spend my days on, rebuilt from scratch against a public specification: take a handful of dimensions, generate real geometry, fold it in a browser, and let anyone poke at it.
FEFCO is the European Federation of Corrugated Board Manufacturers, and its code system is the shared vocabulary of the packaging industry. 0427 is a roll-end tray with a tuck front, which is the box most e-commerce orders arrive in. It is more interesting than the standard 0201 shipping carton because the ends roll inward through several creases and lock, so the fold has real ordering and real constraints rather than four flaps meeting in the middle.
The geometry
Every panel is built extending in one direction from its hinge, and folds about that hinge only. Nesting does the rest: the lid is a child of the back wall, the tuck is a child of the lid, the lock tab is a child of the roll panel. Fold the parent and the children come with it, which is exactly how the board behaves.
The flat blank is derived from the same numbers, not measured off the model. Across the die you get the base length plus a side wall, roll panel and lock tab at each end. Along it you get the front wall, base, back wall, lid and front tuck. Those two figures are the blank size shown above the box, and they are what a converter would quote board against.
The fold order
The box does not fold all at once, because a real one cannot. The ends go up first and roll in, since the roll ends form the side walls and capture the long walls. The long walls follow, then the lid comes over, and the tuck goes down at the front last. Each stage owns a slice of the fold slider and eases within it, which is why dragging slowly reads as assembly rather than as one hinge opening.