Origami Tessellation Terms and Definitions

Posted by Madonna Yoder on

While you may already be familiar with origami terms like mountain and valley folds, sinks, squashes, swivels, and rabbit ears, tessellations have a vocabulary of their own.

Unfortunately, the vocabulary of tessellations is not standardized across all tessellation designers and each tessellation book uses different definitions - and different colors and symbols for their diagrams.

This can make it hard to learn, since everyone is saying things in different ways.

I try to stick to consistent definitions throughout my teaching, and to explain my terms in plain English - no math speak.

Here's my list of the most important terms to understand when you're starting to fold tessellations:

Grid: Pattern of evenly spaced folds that are used for referencing other folds in a tessellation

Square Grid: Grid folded in two perpendicular directions, typically on a square sheet of paper


Triangle Grid: Grid folded in three directions with 60 degree angles at each intersection, native to hexagonal paper and also folded on squares and rectangles

45-Degree Grid: Square grid with either half or all diagonals added

Grid (Square/Triangle): Smallest shape outlined by grid lines on a finished grid

Grid Spacing: The distance of one grid line between two neighboring grid lines in another grid direction


Single Diagonal 45-degree Grid: Square grid with one diagonal added through each grid square, forming a checkerboard pattern of alignment

Double Diagonal 45-degree Grid: Square grid with both diagonals added in every grid square

Mountain fold: Fold that forms a ridge on the side of the paper facing you - shown with red solid lines

Valley fold: Fold that forms a trough on the side of the paper facing you - shown with blue dashed lines


Pleat: A pair of parallel mountain and valley folds

Pleat Depth: The number of grid spacings apart that the mountain and valley folds of a pleat are located, typically one spacing


Tube Pleat: A pair of two parallel, mirrored pleats with two grid spacings between the closest folds of the two pleats

Accordion Pleats: Two or more pleats in the same orientation and direction that stack on top of each other in the folded form to make an accordion/fan shape

Pleat Overlap: Two (or more) non-parallel pleats that cross each other, with one pleat completely closed when the second pleat is folded

Twist: Rotationally symmetric interaction of at least 3 pleats, with an interior shape created that is not part of the pleat folds

Pleat Intersection: Interaction of multiple pleats that is not an overlap or a twist (Note: Ben Parker's definition includes pleat overlaps and twists in the category of pleat intersections)

Crease Pattern (CP): Diagram showing where the mountain and valley folds go on the paper to fold an origami pattern; for tessellations this commonly includes a grid in addition to the folds

Tiling: An abstraction of the structure of tessellations where each twist or pleat intersection gets its own box; used to categorize and design tessellations and study their symmetries

Tessellation: Repeating 2-dimensional pattern

Origami Tessellation: Repeating pattern folded from a single sheet of paper


Whew - I think that covers just about everything!

If you'd like to learn more about each of these terms, check out my Tessellation Foundations series where I show how each of these terms are put into practice while teaching the fundamental skills needed to start folding tessellations.

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