A crease pattern (CP) is a diagram that records all crease lines of an origami model on a sheet of paper in its fully unfolded state.

By distinguishing between mountain folds and valley folds, it is used to read the structure of the model itself rather than the step-by-step folding process.

In origami design, a crease pattern functions as a blueprint, allowing the placement of corners and structural strength to be inferred from the arrangement and density of the creases.

A diagonal grid refers to a grid composed of lines that are not parallel to the edges of the paper, but instead run parallel to the diagonal direction (typically at 45 degrees).

Because the reverse side of the paper appears at the corners, creating visible patterns, this grid is well suited for designs that take advantage of inside-out folding.

A corner folded from the edge of the paper.

Forming one corner requires a 180-degree area, making it thinner than an internal corner but thicker than a vertex corner.

It is easy to create a band-like corner that keeps the same thickness to the tip.

Inside-out refers to an expressive and design approach in origami in which the reverse side of the paper, normally hidden on the inside, is intentionally exposed on the exterior.

Rather than treating the back side as merely hidden, this technique actively uses it as a visual element to emphasize patterns and structural features.

A corner folded from inside the paper.

Because forming one corner requires a full 360-degree area, it tends to become thick.

Kado refers to a protruding part formed by folding in origami.

Typical examples include the head, wings, and tail of a traditional origami crane.

The term kado is written in katakana to distinguish it from the geometric concept of an angle, emphasizing its role as a structural and expressive element unique to origami.

A mountain fold is a fold where the crease forms a ridge, with the paper folded so that the crease protrudes upward.

In crease patterns, mountain folds are typically indicated by dashed or dot-dashed lines.

An origami atom refers to a polygon that appears in a crease pattern and contains no crease lines inside it.

In other words, it is a triangular or quadrilateral region in a crease pattern whose interior is free of folds.

Origami atoms function as the smallest indivisible units of a crease pattern, forming the basic building blocks from which larger structures are composed.

An origami molecule is a connected group of multiple origami atoms that function together as a single structural unit.

Origami molecules are composed of several atoms linked by crease lines and can often be folded as a coherent substructure.

By combining multiple origami molecules, more complex origami forms and overall structures can be designed.

A component proposed by Kamiori-Studio for structurally turning paper into a three-dimensional form.

By combining components, complex polygonal shapes can be created.

It is characterized by a semi-three-dimensional form that does not fold flat.

A step fold is a folding technique that creates a stepped or layered structure by folding the paper multiple times at regular intervals.

It produces a sequence of parallel creases, resulting in a terraced or stair-like form.

A structural isotope refers to a group of forms that share the same grid count and a similar overall shape, while differing slightly in their internal folding structure.

Even when the appearance and resulting form are nearly identical, differences in crease connections, fold directions, or locking behavior lead to variations in structural properties.

Especially in designs using polygon components, being aware of structural isotopes makes it possible to systematically understand how changes in structure affect stability, strength, and ease of folding.

A twist fold is a folding technique in which a portion of the paper is folded in a way that rotates around a central point or axis, creating a twisted folding structure.

As mountain and valley folds are arranged radially, the paper rotates during the folding process, giving rise to a twisted configuration.

In origami design, twist folds are an important technique for concentrating directional forces, locking structures in place, and creating configurations with high paper density.

A valley fold is a fold where the paper is folded inward, creating a crease that sinks like a valley.

In crease patterns, valley folds are usually represented by solid lines.

A corner folded from the paper’s vertex.

Forming one corner requires a 90-degree area, making it the thinnest among corners.