Cite as: Jana Dambrogio, Daniel Starza Smith, et al. 2016. Dictionary of Letterlocking (DoLL). Last updated: 30 December 2017. Date accessed: [Date]. Abbreviated on this page: (DoLL 2016). All images except when noted are courtesy of the Unlocking History Materials Collection.

A fold is arguably the most important manipulation in letterlocking, since it is used in every letterlocking category. The resulting physical mark left in the substrate is a crease.



The impression left in a substrate by a fold, especially when that fold is sharply impressed. (DoLL 2017)

“A line segment (or, in some cases, a curve) on a piece of paper” (Demaine and O-Rourke)

Crease vs Wrinkle

In letterlocking, creases are distinguished from wrinkles. Generally, a crease is the sharp mark left in a substrate by the action of folding, whereas wrinkles result from the substrate buckling and bending around a crease. Wrinkles may also point to damage, e.g. by water. Creases are distinguished from folds, which are the manipulations that produce creases. (DoLL 2017)

See also: fold, wrinkle.


Crease assignment

A term used to establish whether a crease was made by folding a substrate towards or away from the person folding. In other words, crease assignment indicates the directionality of the original folds, either mountain or valley. In letterlocking diagrams, short dash lines indicate valley and alternating short long dash lines indicate mountain folds. Where color is available, mountain folds are red, and valley folds are blue, following standard practice in origami (Demaine and O-Rourke 165). If a substrate is turned over, crease assignment reverses. (DoLL 2017)


Crease pattern

“a collection of creases drawn on paper, meeting only at common endpoints, which
may be viewed as a (usually planar straight-line) embedding of a graph” (Demaine and O-Rourke)




1.)To double or bend a substrate over itself. 

“To arrange (a piece of cloth, a surface, etc.), so that one portion lies reversed over or alongside another; to double or bend over upon itself. Also with in, over, together. Often contextually implying repeated action of this kind. to fold up: to close or bring into a more compact form by repeated folding.” (OED, v1, 1a) 

“To bend or turn back or down (a portion of something).” (OED, v1, 1c)

2.) Esp. in letterlocking, to complete the action of folding (see v1, above) by impressing the bend into a sharply defined edge, so that it maintains its new form to some extent.


1.) The transformation in the substrate formed by the action of folding. In DoLL, the many forms that folding produces are defined separately. (See below.)

“A bend or ply, such as is produced when any more or less flexible object is folded” (OED, n3, 1a).

2.)    A mark or indentation left in a substrate after it has been folded; the physical evidence of manipulation (as in v2, above). Although this term is available, in letterlocking we prefer crease.

Types of folds are displayed below. 


Accordion Fold a.k.a. Zig Zag Fold

A series of alternating and repeating mountain and valley folds that resemble the bellows of an accordion. Also called a zig-zag fold. A Z-fold, which has only three panels, is the simplest kind of accordion fold, though there is no upper limit. In letterlocking, the panels created by the folds may have patterns that are uniform or be irregular. (DoLL 2017)

See also: Z Fold


C Fold

Two parallel folds are made to create three equal-sized panels, with the outer two panels folding in towards one another. When flattened, one outer panel lies on top of the other, with the central panel beneath them. This format is often used today for brochures. (DoLL 2017)

See also: Tri-folds


Catch Fold

A thin fold made along one edge of a substrate. Panels produced by subsequent folding can then tuck inside it. (DoLL 2017)


Corner Fold

A type of diagonal fold originating from the portion of the substrate where two edges meet (e.g., the corner) is pulled towards the center of the substrate creating a diagonal fold. Corner folds can range from small to large, extending across the entire top edge to align with a portion of the left or right edge of a substrate. Distinguished from dog ear, which is not made for paper engineering purposes. (DoLL 2017)

See also: Dog-ear fold, Diagonal fold


Crosswise Fold a.k.a. Short Edge to Short Edge Fold a.k.a. Hamburger Fold

The substrate is folded in half along the middle, short edge to short edge. (DoLL 2017)

See also: Lengthwise fold


Diagonal Fold: A parent term for corner fold, triangle fold, and dog-ear fold. 

Folds that are not parallel to the horizontal or vertical edges of the letter (Witkowski). All corner folds are produced using a diagonal fold, but not all diagonal folds are corner folds. (DoLL 2017)


Directional Fold


Dog-ear Fold

A folded corner of a substrate (usually a page in bound materials), “turned over or creased by repeated or careless use, or to mark a place.” (OED n, 1.)

See also: Diagonal fold, Corner fold


Double Parallel Fold

A manipulation in which “the paper is folded in half and then folded in half again with a fold along the same axis as the first fold. One-half of the sheet of paper is nested inside the other half” (Bear).  


Flattened Folds

The result of when the crease assignment information (mountain or valley) is no longer visible with the naked eye. The image shows a letter model with the upper portion of crease assignments in the the substrate preserved while the creases in the lower portion are indistinguishable. (DoLL 2017)


French Fold a.k.a. Quartered Fold

The paper is folded in half and then in half again with a fold perpendicular to the first fold. “A French fold is a sheet that is folded vertically and then horizontally”. (Master Printing and Mailing)  


Gate Fold and Closed Gate Fold

Outer panels from opposing edges of the substrate are folded towards the center of a larger central panel, creating the effect of two gate doors swinging shut. In a “closed gatefold” the opposing panels meet in the center. A “double gatefold” results when the two folded halves are folded together. (Witkowski 185; Bear)


Independent Folding

When one leaf of a bifolium is folded differently from the other (in other words, the opposite of tandem folding). When unfolded, the crease patterns on each leaf will differ. (DoLL 2017)

See also: Tandem Folding


Lengthwise Fold a.k.a. Long Edge to Long Edge Fold a.k.a. Hot Dog Fold

The substrate is folded in half, long edge to long edge.  (DoLL 2017)

See also: Crosswise fold


Margin Fold

A type of edge fold, the crease of which serves as a margin line for the body of the letter when unfolded. (DoLL 2017)


Mountain Fold

Mountain fold: A fold that is concave upwards when the substrate is laid flat.  /\ See crease assignment.  Crease assignments such as a mountain fold are requisite information needed in order to repeat a crease pattern. (DoLL 2017)

See also: Crease assignment, Valley fold


Pushed-in Fold


Roll Fold

A series of repeating mountain folds that are made by folding the substrate over itself in one direction. When a single sheet is folded in this fashion and opened flat, the folds on one side will be mountain folds and the folds on the other will be valley folds. One sheet is folded and portions of that sheet do not overlap but are folded in the same direction as many times as possible. However, when this action is performed on a folded sheet of paper (such as when the leaves of a bifolium are folded in tandem and rolled) there are a combination of mountain and valley folds created when the substrate is unrolled, unfolded, and laid flat. (DoLL2017)


Signature Box Fold


Tandem Folding

When multiple leaves of substrate lying on top of each other are folded together simultaneously and therefore bear identical crease patterns. Tandem folding is often seen on the two leaves of a conjugate bifolium. The opposite of independent folding. (DoLL 2017)

See also: Independent Folding


Tri-folds: A parent term for C-fold and Z-fold. A family of folds in which a substrate is folded twice to create three panels.


Triangle Fold

See also: Diagonal fold


Valley Fold

A fold that is concave downwards when the substrate is laid flat. \/ (DoLL 2017)

See also: Crease assignment, Mountain fold


Z Fold

See also: Accordion Fold, Tri-folds



A planar deformation that occurs as a by-product of folding, especially in the case of intersecting or multi-layer folds. In letterlocking, wrinkles can be distinguished from folds, since folds are ridges made in a substrate in order to engineer a letter packet, and wrinkles signal the substrate’s natural response to manipulation. (DoLL 2017)

See also: crease and fold.

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