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Chapter 2

THE MOUNTAIN FOLD

The second basic fold in origami, the mountain fold, does not come as naturally or as intuitively as the first one, the valley fold. But from a technical point of view, the mountain fold is not complicated. In this chapter, as in the first, you will learn the symbols associated with the mountain fold and find tips and a trick for creating it. At the end of the chapter, as in all the others, the concepts you learn will be “translated” into folds to create a model—in this case, a rectangular box.

TOPICS AND SYMBOLS

Mountain fold indicated by dashes and dots
Arrow indicating the direction of a mountain fold
Hidden edges
Repetition
Enlarged view
Reduced scale

PRACTICE MODEL

Place Card Holder

The Mountain Fold Line

The mountain fold is indicated by a row of dashes alternating with dots. The width of the fold line is roughly 0.5 mm. Compare the shape of the mountain fold in fig. 4 below with the valley fold in fig. 2 on page 7.

The mountain fold is the exact opposite of the valley fold. In the mountain fold, however, the entire sheet of paper must always be lifted because the fold is done “backwards.” If we take a sheet of paper on which a mountain fold has been made and then flatten the fold, we can easily see that a peak has formed along the crease created by the fold. This feature, enlarged in fig. 4, resembles the image of a mountain from which the fold derives its name.

The Arrow Indicating the Direction of a Mountain Fold

The arrow used to indicate a mountain fold is very different from the one indicating a valley fold. Its tip resembles a harpoon, but the harpoon is not completely attached to the shaft. The arrow is often “clipped,” that is, its point lies partially hidden behind the paper’s surface while indicating the direction the fold will take. Here are a few examples.

In this graphic representation of a mountain fold, the top edge of the paper is folded backwards to meet the bottom edge. The tip of the arrow indicating the maneuver is hidden behind in order to reinforce the concept of a mountain where the back is hidden from view.

In practice, it is much easier to make a mountain fold by flipping the paper over so that its white surface is visible, and then folding it like a valley fold. Once the fold is completed, the sheet can be stood up as in fig. 3 with its edges at the bottom. Note, however, that it is not always possible to execute a mountain fold in this way.

Here are other applications of the mountain fold symbol.

Although we suggested on page 14 that a mountain fold can be made by forming a valley fold and then turning it upside down, this is not always possible, as the example below shows.

In this example, it is useless to turn the sheet upside down. You would have to unfold the upper layer, make a valley fold, and then return to the previous position in order to reach the desired orientation.

The Hidden Edge Line

A fine dotted line is used to indicate the location of an edge that is not visible. When necessary, the hidden edge, as in fig. 1, is represented as in fig. 2.

In general, all hidden objects are drawn with a dotted line starting at the point at which they disappear from view. The same applies to arrows.

Fig. 1 requires that the white sheet be tucked beneath the colored layer. The arrow indicates the order to be followed. At the point where the arrow passes beneath the colored layer and thus becomes hidden from view, its line becomes dotted. In fig. 2 one can easily deduce that the dotted line represents that part of the white sheet that has been inserted beneath the colored layer.

The Repetition Symbols

The “repeat arrow” is another symbol that you will come across in the model at the end of this chapter. For example, in order to fold four corners towards the center of a square, the same move must be completed four times. Usually the first fold is indicated by a complete arrow. A short, straight arrow with three perpendicular marks on the shaft indicates that the same fold must be repeated three more times.

If a fold needs to be made on only two corners of a square, the first fold can be indicated by a complete arrow and the second by a short arrow with one perpendicular mark. The number of marks indicates the number of times the fold must be repeated. Thus, for example, if the corners of an octagon need to be folded towards the center, the first arrow may be depicted along with another arrow with seven perpendicular marks. The repeat arrow may also be applied to an edge.

Repetition can also be applied to an entire sequence of steps already completed. In such cases, an arrow with a single perpendicular mark is paired with the numbers of the steps to be repeated.

The meaning of the directions here is to repeat steps 4–7.

The Enlarged View Symbol

“Enlarged view” is another important origami symbol. It indicates that the figure which the arrow is pointing at is no longer to scale but is enlarged. It is used when the dimensions of the figure become too small for the instructions to be read properly. It can also be used to clarify certain details, such as the number of superimposed layers, or to highlight the instructions for carrying out a particular fold.

Enlargement may be applied to only a portion of an illustration. In such cases, the enlarged part is usually highlighted in a circle or oval, as in the figures below.

The Reduced Scale Symbol

Sometimes the opposite may occur. When an illustration becomes too large, a “reduced scale” arrow is used.

Recommended paper size: 6¾ x 9¼ inches (17 x 23.5 cm)—A4 format works as well

Crease pattern showing the finished model’s folds

The initial sheet of paper and the final model juxtaposed

Practice Model:

Rectangular Box

Make a valley fold, bringing the right over to the left edge, and then unfold.

Make two valley folds, bringing the right and left edges to the central crease, and then unfold.

Make a valley fold, bringing the bottom to the top edge, and then unfold.