Folding Screen

Natural origami

Flat folding


Mountain-valley counting.

Sides around a vertex.

The building of origami designs may also be shown as crease patterns. The most important questions about such crease patterns are whether a crease structure are folded to an appartment design, and whether determining just how to fold them is an NP problem. Associated problems if the creases are orthogonal are known as chart folding problems. There are four mathematical rules for producing flat-foldable origami crease patterns:

crease habits are a couple of colorable

at any vertex the number of valley and hill folds always differ by two either in direction

Kawasaki’s theorem: at any vertex, the sum of the all the odd angles adds up to 180 degrees, as do the even.

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