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Tessellation (origami)

An origami tessellation is a repeating geometric pattern folded across a whole sheet, usually from a grid of creases with twist folds and pleats.

Most tessellations begin by folding a precise grid of squares or triangles into the paper. Twist folds, where a small polygon rotates as its surrounding pleats collapse, are then made one by one across the grid, so the pattern repeats like tiles. Held up to the light, many tessellations show striking patterns created by the overlapping layers.

Accuracy is everything: a small error in the grid spreads across the whole sheet. Start with a small grid in thin, crisp paper, crease every line in both directions, and collapse one twist at a time. Tessellations are closely linked to the mathematics of folding and are a good next step for folders who enjoy geometry.

How to fold your first tessellation

  1. 1

    Start with a thin, crisp square of at least 15 cm; kami works well.

  2. 2

    Fold a grid by halving: halves, then quarters, then eighths, in both directions, creasing each line as a valley and then as a mountain.

  3. 3

    Add any diagonal creases the pattern needs, again in both directions.

  4. 4

    Collapse the first twist fold: pinch the pleats around one small square so they rotate together, and press the square flat.

  5. 5

    Move to the neighboring part of the grid and collapse the next twist, keeping the pleats parallel.

  6. 6

    Continue across the sheet one twist at a time, then flatten the whole piece.

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Common mistakes and how to fix them

  • The pattern drifts out of line

    The grid is inaccurate, and errors repeat across the sheet. Divide by folding, halves to quarters to eighths, rather than by measuring.

  • The twists won’t lie flat

    The grid creases must bend both ways. Re-crease them in both directions before collapsing.

  • The paper tears where pleats meet

    Many layers meet at the corners of each twist. Use thin paper and collapse gently.

Good to know about tessellations

Tessellations became a recognized branch of origami in the second half of the twentieth century. The Japanese mathematics teacher Shuzo Fujimoto published many early twist-fold patterns, and later designers have created thousands more. A finished tessellation can be displayed flat, framed against a window, or folded in metallic or translucent paper as a decoration. Because each pattern repeats one small unit, tessellations are a calm, meditative kind of folding: once the grid is ready, the same twist is made again and again across the sheet. Start with a small grid of square twists before moving on to triangles and hexagons.

Tessellation: questions

What paper is best for tessellations?+

Thin, strong paper, because many layers overlap. Kami is fine for small practice grids, and translucent paper shows the patterns beautifully when held up to the light.

Are tessellations related to math?+

Closely: they come from the geometry of folding, and grids, angles and symmetry decide which patterns are possible. They are a good next step for folders who enjoy geometry.

How long does a tessellation take?+

The grid alone can take longer than the twists. A small practice piece is an evening’s project, while large and complex tessellations can take many hours, which is part of their appeal.

Related folds and bases