Folding Techniques

Origami and Paper Folding

Course 1 · Chapter 4 · Folding Techniques: Reverse, Squash, Petal and Sink

In Origami and Paper Folding 3 you borrowed three techniques without much explanation: the inside reverse fold for the crane's neck and tail, the squash fold for the frog base, and the petal fold for the bird base. This chapter slows down and teaches them properly, adds a fourth (the sink), and then puts them to work in the flapping bird. These four moves, plus the valley and mountain folds you already own, are behind most traditional models. Once your hands know them, a diagram stops being a puzzle and becomes a recipe.

The Technique Family at a Glance

Every technique here is really a valley and a mountain fold done together on layered paper, with a specific crease-first, collapse-second rhythm. Here is how they compare. Descriptions are simplified, and different books vary slightly in naming (check yours).

Technique	What it does	Crease first?	Typical use
Inside reverse fold	Tucks a point into the model, so the point swings the other way	Yes, fold and unfold	Necks, legs, tails, beaks
Outside reverse fold	Wraps a point around the outside of the model	Yes, fold and unfold	Heads, feet, folded-back tails
Squash fold	Opens a flap and presses it flat into a new shape	Usually a single crease	Frog base, widening a flap
Petal fold	Lifts a layer into a long, narrow point	Yes, three creases	Bird base, lily, flower petals
Sink fold	Pushes a point or corner down into the model	Yes, essential	Tidy tips, bases, box corners (check)

The Reverse Folds

A reverse fold changes the direction a point is facing. You make a diagonal crease across a narrow flap, open the flap slightly, and then push the tip so that the crease reverses and the point folds over onto itself. The difference between the two kinds is simply where the folded part ends up: inside the model, hidden between its layers, or outside, wrapped around it.

The Inside Reverse Fold

This is the one you used for the crane. Practise it on a plain flap, such as one half of a kite base, before using it on a model.

Fold the flap the way you want the point to go. Crease firmly along the line where the bend will be, then unfold. A sharp crease matters more here than anywhere.
Open the flap slightly. Gently separate the two layers of the flap at the tip, like opening a book a few degrees.
Push the tip in and up. Hold the crease and push the tip towards the inside of the model. The crease turns inside out, and the point swings over onto the other side.
Flatten. Press the whole shape flat, checking that the two sides of the reversed section are mirror images.

The Outside Reverse Fold

The outside reverse fold uses the same crease but the opposite move. Instead of pushing the tip inside, open the model along its spine and wrap the tip around the outside, so the point wraps round the outer layers. It is the move behind many heads and beaks, where you want a clean outer surface with no visible inner layers.

Inside or outside? Look at the crease If the crease you made is a valley fold when seen from the front, you are about to make an inside reverse fold. If you are about to wrap, the central spine becomes the hinge and the crease flips to the other side. When a diagram's arrow points into the model, the fold goes inside; when it wraps around, it goes outside (check the arrow convention you learned in Origami and Paper Folding 2).

The Squash Fold

A squash fold does what the name says: you open a flap and press it flat so it spreads sideways into a new shape, usually a square or a diamond. The frog base is made of four of them.

Make the crease line. A squash fold needs one crease from the base of the flap up through its middle. Fold the flap in half along its centre line and unfold.
Lift the flap. Open the flap and slide a finger inside, lifting its upper layer.
Press down. Push the lifted layer to one side. Because the centre line is already creased, the layer lands in a neat symmetric shape.
Flatten and check. The edge that was on the centre line now lies along the side, and the top is a clean point.

Uneven squashes A lopsided squash usually means the centre crease was not sharp, or the flap was lifted off-centre. Unfold, re-crease the centre line, and try again. A flap that is too thick to squash neatly is a hint to use thinner paper, which we come back to below.

The Petal Fold

The petal fold is a squash and a reverse fold in one collapse. You met it in outline in Origami and Paper Folding 3. Here it is again, step by step, with the reasoning behind each crease.

Start from the preliminary base with the open end pointing towards you and the closed point at the top. Work on the front layer.
Kite-fold the front layer. Fold the two lower edges in to meet the centre line, crease firmly, and unfold. These creases tell the paper where the side edges will go.
Mark the hinge. Fold the top triangle of the front layer down over the kite folds, crease across the line where the side creases cross the centre line, and unfold.
Lift and collapse. Lift the bottom corner of the front layer up. As it rises, the top crease hinges, and the two side creases fold in. Flatten and a narrow diamond appears.
Repeat on the back. Turn over and make the same petal fold.

The crease map below shows the front layer opened out, with the three creases and the point that rises:

# Front layer of the preliminary base, shown for the petal fold
# \ and / = kite creases (valley)    - = hinge crease (valley)
# the bottom corner is lifted up to the hinge

          /\
         /  \
        /    \
       /      \
      /--------\ <- hinge crease
     / \      / \
    /   \    /   \
   /     \  /     \
  /_______\/_______\
          ^
      lift this corner

The Sink Fold

A sink fold pushes a corner or a point down into the body of the model so that it vanishes inside, leaving a flat or slightly dented top. It is the most advanced of the four: the creases around the point have to flip from mountain to valley all at once. You do not need it for the flapping bird, but you should try it once now, because it appears in later chapters.

Fold the corner over. Fold the point down to the depth you want it to sink, crease firmly, and unfold. This crease marks the bottom of the dent.
Crease the sides. Pre-crease the edges of the shape that will fold in, so that the sunk part forms a small triangle of valley folds inside.
Open slightly and push. Open the layers a little and push the point inwards. The creases around the dent flip from mountain to valley.
Collapse flat. Press the model flat. If it will not collapse, one crease is not flipping, so find it and flip it by hand.

An easy practice sink Practise on a preliminary base. Fold the top point down, crease, unfold, and then push the point in. Because every layer is the same shape, you can see what flips. It gets easier on the second try.

Precision and Tidiness

A good fold is not just about the right move. It is about the same small habits, repeated on every crease. Here are the ones that matter most, roughly in order of payoff:

Line up edges before you crease. Hold the edges together, check from above, and only then press the crease.
Crease from the middle outwards. Start in the centre of the fold and drag your thumbnail towards the edge, so the paper cannot slip.
Fold on a hard, flat surface. A table, not a pillow or a cloth.
Fold as few layers at once as you can. Each layer adds a little thickness.
Unfold and refold a bad crease once. A second try is better than a third, because paper fibres tire.

Why Layers Matter: A Little Arithmetic

Each fold doubles the number of layers where the paper is folded flat. Paper is thin, but the doubling adds up fast. This script assumes ordinary copy paper, about 0.08 mm thick (check the thickness of your own paper), and also shows how small errors add up:

t = 0.08
for n in range(1, 8):
    print('Folds', n, '-> layers', 2**n, '-> stack', round(2**n*t, 2), 'mm')
print()
err = 0.5
for n in (1, 2, 4, 8):
    print(n, 'creases:', n*err, 'mm of drift')

Output when run:

Folds 1 -> layers 2 -> stack 0.16 mm
Folds 2 -> layers 4 -> stack 0.32 mm
Folds 3 -> layers 8 -> stack 0.64 mm
Folds 4 -> layers 16 -> stack 1.28 mm
Folds 5 -> layers 32 -> stack 2.56 mm
Folds 6 -> layers 64 -> stack 5.12 mm
Folds 7 -> layers 128 -> stack 10.24 mm

1 creases: 0.5 mm of drift
2 creases: 1.0 mm of drift
4 creases: 2.0 mm of drift
8 creases: 4.0 mm of drift

Two lessons come out of this. First, seven simple folds in the same place would already give a stack about a centimetre thick, which is why models never do it, and why thin paper is kinder to complicated models. Second, a half-millimetre slip on each crease looks harmless, but after eight creases the model is out by 4 mm and the last folds will not meet. Accuracy early in the sequence is worth far more than accuracy at the end.

Your Fourth Model: The Flapping Bird

The flapping bird is the classic traditional model that moves: pull the tail gently and the wings flap. It is built from the bird base (Origami and Paper Folding 3) and uses an inside reverse fold for the neck and another for the head. Use a 15 cm square, coloured side up to start.

The Steps

Fold the preliminary base, then the bird base: petal fold the front, turn over, petal fold the back. The two long, narrow points hang at the bottom and the closed point is at the top.
Check the layers. The bird base has a split at the bottom: two narrow points that are the neck and the tail. The two upper flaps on each side are the wings.
Narrow the neck and tail. If your base has loose edges, fold each lower edge of the two long points in to the centre line, front and back, so they are slim (check against your diagram).
Make the neck (inside reverse fold). Pick one long point, crease it up at a steep angle, unfold, open, and push it up inside the model. It now points upward and slightly backward.
Make the tail (inside reverse fold). Do the same with the other long point, so it points up on the other side. Make the two points roughly the same length.
Make the head. On the neck, make a small inside reverse fold at the tip, folding the point down for the beak. Keep the crease small.
Make the wings. Fold the two wing flaps down on each side so they lie out from the body, one front and one back, then bring them back up slightly so they stand open.
Make it flap. Hold the bird by the point where the neck and body meet, with one hand, and gently pull the tail straight down with the other. The wings move up and down. Release and they relax.

If the wings will not move The wings flap because the body can bend at the join. If it will not flap, the neck or tail folds may be too tight, or the wings may be creased too sharply near the body. Soften the crease with a thumb and try again (check by comparing with a bird that flaps).

Challenges

Each challenge has a worked solution you can open after you have tried it.

Challenge 1

Take a square of scrap paper and fold a preliminary base. On the front layer practise the inside reverse fold: fold up one of the narrow points, crease, unfold, open and push it in. Then do the outside reverse fold on a different point of the same model. Say in your own words how the two results look different.

→ Solution

Challenge 2

Fold a bird base, then open it out and look at the creases. How many petal folds were made, and how many creases does each petal fold use? Then change the script above so the paper thickness is 0.1 mm, and say how many folds it takes before the stack goes beyond 10 mm.

→ Solution

Challenge 3

Fold the flapping bird from a 15 cm square. When it is finished, test it: does it flap smoothly? If not, find out why and fix it. Then fold a second bird from a 10 cm square and compare. Which was easier to fold accurately, and which flaps better?

→ Solution

Quick Reference

Inside reverse fold: crease, unfold, open, push the point into the model
Outside reverse fold: the same crease, but the point wraps around the outside
Squash fold: open a flap and press it flat along a centre crease
Petal fold: three creases, lift the corner, collapse into a long point
Sink fold: push a point down into the model; the creases flip
Precision: line up, crease from the middle out, fewest layers possible
Fourth model: the flapping bird, from the bird base

Next, in Origami and Paper Folding 5, we put these techniques to work on animals: turning flaps into legs, heads and tails, and folding a fox, a rabbit and a jumping frog.