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Origami Design Secrets: Mathematical Models for an Ancient Art

Written by Robert Lang.

1: Introduction

It is easier to replicate an origami figure then to design it.
There are only tricks from which you can pick, there is no cookbook, a sure way to fold any shape.

2: The Building Blocks of Origami

Three types of folds: mountain, valley and crease.
Creases are undone folds.
Folds can be sharp or soft.

2.1 Symbols and Terms

Diagrams are the system of folding instructions for origami.
Words "up" or "down" refer to the paper on the table.
"Near" and "far" mean the layer nearest and further from you.
Other words that'll be used are "corner", "folded edge", "raw edge", "tip", "spine", ...

Origami diagrams are line drawings.
Five types of lines:

  • paper edges, raw or folder are solid lines
  • creases are thin lines and will often stop before they reach the edge of the paper
  • valley folds are dashed lines
  • mountain folds are chain lines (dot-dot-line)
  • hidden layers are shown as "x-ray" or dotted line

Looped arrows tell you to flip the paper: either side to side or from top to bottom.
Rotation is plane is shown as a clock.
If you need to repeat a series of steps, you will see them in a box.

2.2 Basic Folding Steps

Valley fold.
Mountain fold.
Simultaneous valley and mountain fold.
Unfolding is common too.
Fold-unfold step is often indicated by a single instruction.

The crease pattern shows a lot about the model you will be building.
Mountain and valley folds are either shown as chain and dashes or as solid black and solid colored lines.

Inside and outside reverse fold is when you push a tip away from the spine to create a valley or mountain fold.
If the instruction is "reverse fold", inside reverse fold is implied.

Rabbit ear fold is most often performed on a triangular flap when you push the angle bisector down. Reguardless of triangle, all edges will lie on the same line.
There are two common rabbit ear variations.

Squash fold is when you spread the flaps and then squash them.
There is a variation of this fold.

ToDo

3: Elephant Design

The elephant is the hello world program of origami.
Origami is the art of suggestion. Unlike paintings, origami can never truly represent its subject.

Origami have a large spectrum of complexity.
It is not easy to explain an origami's elegance.
Efficiency is closely related to elegance.

3.1 Elephant Design 1

A simple 5 fold Elephant Head.

3.2 Elephant Design 2