📐 FlatForge

A real case · you decide

Ines checks a fold before it is cut

Ines, 17 — an intern at a small design studio, asked to check a crease pattern before it goes to a cutting machine

The idea in play: a crossing folds flat only if its alternate angles each sum to 180° (Kawasaki–Justin) and its mountains and valleys differ by two (Maekawa) — and every smallest sector is a mountain–valley pair.

The studio is making a folding lampshade from thin plastic. A file arrives from the client with a note: "Our software says it folds flat — please send it to the cutter today."

Ines zooms into one crossing. Four creases meet; the angles around it read 45°, 90°, 135° and 90°. The file marks three mountains and one valley.

The cutter is expensive to run and the plastic does not forgive: a wrong crease means a sheet in the bin. She has the theorems, and she has the file. The client has a deadline.

Ines's note goes into the studio's checklist: name the rule, name the crease, and say what a local check cannot promise.

Check a crossing yourself →