Reading Diagrams

Origami and Paper Folding

Course 1 · Chapter 2 · Reading Diagrams: Symbols, Steps and a Simple Box

In Origami and Paper Folding 1 you learned the two folds everything is built from, and you folded a boat by following a written list. Written lists get clumsy quickly, because "fold the lower-left corner of the top layer up to the midpoint of the right edge" is hard to follow and impossible to translate. Folders solved this long ago with a shared picture language. Once you can read it, you can fold from any book or website, in any language, without a teacher. This chapter teaches that language, the handful of names for the common starting folds, and finishes with a simple box.

Why Diagrams Beat Words

A diagram shows you the paper before the step, with a line and an arrow that say what to do to it. The next picture shows the result. If your paper matches the picture, you are on track, and if not, you spot the mistake straight away instead of ten folds later. The standard set of symbols is usually called the Yoshizawa-Randlett system, after the Japanese master Akira Yoshizawa, who developed the conventions, and Samuel Randlett, who helped bring them to a wider audience in the 1950s (check the exact dates and credits). Almost every modern book uses it, with small variations.

A reading habit worth building Look at the next picture before you fold. The picture after the step shows where the paper should end up, and that makes the instruction much clearer than the line and arrow alone.

The Symbols You Need

You already know the first two. The rest are quick to learn, and a small set covers most beginner models. Small drawing details differ between books (check yours), but the meanings below are standard.

Symbol	Drawn as	Meaning
Valley fold line	Dashed line: - - - - -	Fold the paper toward you so the crease sinks
Mountain fold line	Dash-dot line: - . - . - .	Fold the paper away from you so the crease points up
Existing crease	Thin solid line	A crease you made earlier, or an edge of a folded layer
Fold arrow	Curved arrow ending in the place the paper moves to	Move the paper along the arrow (a solid head usually means valley, a hollow head mountain; check your source)
Fold and unfold	Arrow that goes there and back	Make a crease, then open the paper again (a pre-crease)
Turn over	Arrow looping over a short line	Flip the paper sideways, like turning a page
Rotate	Circular arrow	Turn the paper round on the table by the amount shown
Hidden edge	Dotted line	An edge or fold that is behind the top layer (an X-ray view)
Equal marks	Matching small ticks on two lengths	These two distances are the same
Repeat	A number beside an arrow, such as "x2"	Do this step on the other side, or the given number of times

# The two fold lines, drawn the way a diagram draws them

 Valley fold      - - - - - - - - - -
 Mountain fold    - . - . - . - . - .
 Existing crease  ----------------------
 Hidden edge      . . . . . . . . . . .

# Fold and unfold: the arrow goes out and comes back
        .---------.
        |         v
 ------- - - - - - - ------

Reading a Step Sequence

A model is a list of numbered pictures. Each picture shows the paper as it is now, plus what to do next. Here is how to read one, using a step you already know from the boat.

Find the paper in the picture. Compare it with your own: which corner is where, which side up?
Find the line. Is it dashed (valley) or dash-dot (mountain)? That tells you which way to fold.
Follow the arrow. The tip shows where the edge or corner lands. If the arrow tip touches a corner or an edge, line them up exactly.
Check the next picture. Your paper should now look like it.

# One step, read as a before and after

 Step 3                               Step 4
 valley fold the right edge           the result
 to the centre line

 +--------+--------+                  +--------+----+
 |        :        |                  |        |    |
 |        :     <--+                  |        |    |
 |        :        |                  |        |    |
 +--------+--------+                  +--------+----+
          :  centre line (existing)

Notice What Stays the Same

Anything the diagram does not change stays as it was. Beginners often re-fold or flatten something that has not been mentioned. If a step does not say to turn the paper over, do not turn it over. If a step says to "repeat on the other side", it will say so with an arrow or a number.

The Base-Fold Vocabulary

A lot of models begin with the same few folds, so folders gave them names. Knowing these names makes instructions shorter ("fold a blintz") and lets you spot patterns between models. Names vary between books (check), but these are the most common.

Name	What you do	Result
Book fold	Fold the paper in half edge to edge, like closing a book	A rectangle, half the area
Triangle fold	Fold the paper in half corner to corner	A right-angled triangle
Cupboard fold	Fold two opposite edges in to meet the centre line, like cupboard doors closing	A rectangle with the doors in front
Kite fold	Fold two edges that meet at a corner onto the diagonal	A kite shape
Blintz fold	Fold all four corners to the centre	A smaller square, turned 45 degrees

You will meet the larger bases, such as the preliminary base and the bird base, in Origami and Paper Folding 3. They are all built from these simpler folds.

One fact is worth knowing before you start: every time you fold something in half, you double the number of layers and halve the width. A short script makes the growth clear.

for n in range(0, 5):
    print('folds in half:', n, '  layers:', 2 ** n, '  strip width of a 210 mm square: %.1f mm' % (210 / 2 ** n))

Output when run:

folds in half: 0   layers: 1   strip width of a 210 mm square: 210.0 mm
folds in half: 1   layers: 2   strip width of a 210 mm square: 105.0 mm
folds in half: 2   layers: 4   strip width of a 210 mm square: 52.5 mm
folds in half: 3   layers: 8   strip width of a 210 mm square: 26.2 mm
folds in half: 4   layers: 16   strip width of a 210 mm square: 13.1 mm

Why you can't fold forever Four folds in half already gives 16 layers, which is why thin paper matters and why thick printer paper fights you in complex models. This is also why the preliminary steps in advanced models are done in a fixed order, so you never have to fold through more layers than you have to.

Your Second Model: A Simple Box

Here is a small open box folded from a single square, with no cutting or glue. It is built entirely from the vocabulary above: a few pre-creases (fold and unfold), then a fold that raises the walls. Use a 15 cm square of origami paper, or make a square from A4 as in Origami and Paper Folding 1. The box has a square base half the width of the paper, and walls a quarter of the width high.

for s in (150, 210):
    print('Square', s, 'mm -> creases at +/-', s / 4, 'mm from centre; base', s / 2, 'x', s / 2, 'mm; walls', s / 4, 'mm high')

Output when run:

Square 150 mm -> creases at +/- 37.5 mm from centre; base 75.0 x 75.0 mm; walls 37.5 mm high
Square 210 mm -> creases at +/- 52.5 mm from centre; base 105.0 x 105.0 mm; walls 52.5 mm high

The Crease Map

Before folding, here is the finished crease pattern, as a diagram would draw it. The middle square becomes the floor, the four strips around it become the walls, and the four corner squares are the spare paper that gets tucked in.

# Crease map, looking at the paper. 4 x 4 grid of equal squares.
# F = floor, W = wall strip, C = corner square (tucked in)

 +-----+-----+-----+-----+
 |  C  |  W  |  W  |  C  |
 +-----+-----+-----+-----+
 |  W  |  F  |  F  |  W  |
 +-----+-----+-----+-----+
 |  W  |  F  |  F  |  W  |
 +-----+-----+-----+-----+
 |  C  |  W  |  W  |  C  |
 +-----+-----+-----+-----+

 Valley folds: the four lines around the floor
 Each corner square also has its diagonal crease

The Steps

Pre-crease the diagonals. Start with a square, coloured side down. Fold it in half corner to corner (triangle fold), crease, and unfold. Repeat with the other diagonal. Unfold completely. These diagonal creases will run through all four corner squares.
Pre-crease the centre lines. Fold the square in half edge to edge (book fold), crease, and unfold. Repeat in the other direction. You now have a plus sign and an X of creases.
Find the quarter lines. Fold the left edge in to the centre crease, crease it, and unfold. Do the same with the right edge, then the top, then the bottom. Each of these folds is a valley fold on the coloured side. The paper now carries a 4 by 4 grid of creases, like the map above.
Raise two walls. Stand up the left and right wall strips so they are vertical. The corner squares at the ends will want to buckle in the middle: that is the diagonal crease at work.
Raise the other two walls. Lift the top and bottom strips up, and as you do, fold each corner square in half along its diagonal so it makes a small triangle, pointing into the box.
Tuck the corners. Fold each corner triangle flat against the outside of the nearest wall, and press the wall down along its crease so that it stays. Which way each corner tucks (inside or outside) depends on the paper, and either works (check which looks neater with yours).
Square up the box. Run a finger around the inside of the floor to sharpen the corners, and flatten the base on the table.

Why this box matters The same box with a slightly larger square makes a lid that fits over it. You will build both, along with other boxes, in Origami and Paper Folding 6. For now, notice how the crease map came first: reading a crease map is the key skill behind every model in this course.

Challenges

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

Challenge 1

Here are three diagram steps written out in words. Rewrite each as the symbols a diagram would use (line type, arrow, extra marks): (a) fold the bottom edge up to the top edge, then open it out again; (b) fold the left corner behind the paper to the centre; (c) turn the paper over, then rotate it a quarter turn clockwise.

→ Solution

Challenge 2

Fold the simple box from a square of any size. Measure the base and the wall height with a ruler, and compare them with the numbers the script would give for your square. Then change the script to print the base and wall height for a 100 mm square and a 200 mm square, and say what happens when the paper is twice as wide.

→ Solution

Challenge 3

Go back to the paper boat from Origami and Paper Folding 1. Write the first three folds as a diagram description in words and symbols: for each step, name the base-fold from the table (if one applies), the line type, and what the picture afterwards should look like. Then give your list to someone, or read it back yourself a day later, and fold from it alone.

→ Solution

Quick Reference

Valley: dashed line. Mountain: dash-dot line
Existing crease: thin solid line. Hidden edge: dotted line
Fold and unfold: arrow there and back, makes a pre-crease
Reading a step: find the paper, find the line, follow the arrow, check the next picture
Base folds: book, triangle, cupboard, kite, blintz
Layers: each fold in half doubles them
Second model: simple box, base half the width, walls a quarter high

Next, in Origami and Paper Folding 3, we meet the classic bases (kite, fish, bird and frog, plus the preliminary base) and fold the crane, the model most people think of first when they hear the word origami.