How to Change Pleat Direction Across Decorative Paper Tiles

First decide whether you want to change the direction of the visible ridges, the way a folded flap lies, or the face of the paper on display. These are different adjustments.

A mountain fold forms a ridge on the face you are viewing; a valley fold forms a trough. A simple pleat combines parallel mountain and valley folds. Designer Madonna Yoder explains these terms, including pleat depth, in her Origami Tessellation Terms and Definitions.

For an arrangement of separate tiles, use this decision table before changing any creases:

Desired change	Adjustment	What to check
Vertical ridges become horizontal	Rotate the tile 90° on the work surface	The tile’s footprint still fits its space
A directional motif points the opposite way	Rotate the tile 180°	Parallel ridges retain the same axis
The reverse face becomes visible	Turn the tile over	Paper color and visible fold structure may change
A pleat flap lies toward the opposite side	Test a revised fold arrangement on a spare piece	Rotation alone may not produce the intended result

The key distinction is between ridge orientation and fold structure. Rotating an intact tile changes its orientation within the panel without requiring you to reconstruct its pleats.

Square tile footprints make quarter-turn arrangements straightforward: the outside dimensions remain the same after rotation. A pleated rectangle does not necessarily retain the same width and height when turned.

For a first project, use four square backing cards with a smaller folded paper element centered on each. The backing defines the tile boundary, so the folded element can change direction without changing the panel grid.

Gather four matching paper squares, four matching square backing cards, a ruler, a pencil, and an adhesive suitable for your selected paper. Keep one additional paper square for testing. These are project choices for the exercise below, rather than specifications from a published folding pattern.

Use the same paper size and crease spacing for all four folded elements. Yoder defines a folding grid as evenly spaced reference folds and pleat depth as the spacing between the mountain and valley folds. Recording those dimensions gives you a useful reference when comparing pieces. See her tessellation terminology guide.

Before making the whole set, fold one sample and place it on a backing card in both orientations. Choose a backing large enough to accommodate both positions with the border you want. Measure the folded sample rather than assuming its finished footprint will equal the starting paper size.

The following illustrative exercise creates four accordion-folded elements. Its measurements are convenient starting points; they are not required dimensions for decorative paper tiles.

1. Start with a 10 cm paper square. Fold it in half, unfold it, and use successive halving folds to divide the same dimension into eight equal strips. Each strip is 1.25 cm wide.
2. Open the sheet. Working from one edge, arrange the seven internal creases so they alternate mountain, valley, mountain, valley, mountain, valley, mountain when viewed from the chosen front face.
3. Close the folds into an accordion, then open them enough to display the repeated ridges. Keep the crease lines parallel.
4. Place the folded element on a 12 cm square backing card. Adjust the accordion opening to leave a visible border, without flattening away the ridges.
5. Make three more elements with the same starting dimensions and fold sequence. Compare each against the first before attaching it.

The British Origami Society’s instructions explain that mountain and valley creases can be made separately, unfolded, and then combined into a pleat. Use that sequence if trying to form the accordion immediately makes crease placement difficult. See Valley & Mountain folds.

At this stage, keep the elements loose. Set a common displayed width by comparing them beside a ruler. Equal starting sheets alone do not establish equal displayed widths when the accordions are opened to different amounts.

Arrange the four backing cards in two rows. Label their backs A, B, C, and D, reading across the top row and then the bottom row. Choose the top edge of the overall panel and keep that reference throughout the project.

For a simple alternating layout, use this map:

Position	Tile	Visible ridge direction
Top left	A	Vertical
Top right	B	Horizontal
Bottom left	C	Horizontal
Bottom right	D	Vertical

Place all four folded elements with vertical ridges first. Then rotate B and C a quarter-turn while keeping their front faces upward. This gives you a repeatable direction change without introducing a second fold pattern.

For a larger panel, continue the same alternating rule across each row and start the next row with the opposite orientation. Draw the whole map before assembly, particularly if you also use different paper colors.

Inspect both the individual tiles and the spaces between them. Decide whether you want separate framed patches of texture or ridges that appear to continue across tile boundaries. The latter requires checking crease positions at the adjoining edges, not just matching the general direction.

Use a dry layout to answer three practical questions: Does every tile show the intended face? Does every quarter-turn fit its allotted space? Are the displayed pleat openings consistent?

Slide neighboring tiles together temporarily. Look along the row and compare the borders around the folded elements. If one element looks wider, adjust its accordion opening before changing the position of the entire tile.

Next, inspect the arrangement from its intended viewing direction. A useful check is to trace the ridge lines with your eyes from top to bottom, then from left to right. Compare what you see with the direction map rather than relying only on the appearance of the shadows.

Test the adhesive on the spare folded piece and a backing offcut, following its application instructions. Check that the chosen contact points hold the element at the opening you want. Attach one complete tile first and inspect it before repeating the attachment method across the set.

If a finished tile needs a quarter-turn, rotate the whole backed unit during panel assembly. Keep its identifying letter on the reverse so you can restore the planned arrangement after moving pieces around.

In an origami tessellation, a “tile” can describe a region within one connected sheet rather than a separate paper component. Yoder’s Tiling-Based Origami Tessellation Design explains how an abstract tiling represents connected twists and their relationships.

You cannot lift and rotate one region of that sheet as you would a loose tile. In the twist-based framework Yoder describes, pleats connect twists with opposite rotation directions. Changing one region therefore requires checking its connections to neighboring regions.

For a continuous-sheet project, follow the designer’s crease pattern and any documented variations. To investigate a direction change, make a small sample containing the changed region and its immediate neighbors. Check the crease assignments, spacing, and folding sequence before extending the variation across a larger sheet.

If your aim is simply to alternate horizontal and vertical decorative texture, separate backed tiles provide a more direct construction method. Choose the continuous-sheet approach when the connected folding structure is part of the result you want.

A half-turn produces little visible change. Parallel ridge lines retain their horizontal or vertical orientation after a 180° rotation. Use a 90° turn to change that axis. A half-turn is useful when an asymmetric detail needs to point the other way.

The paper color changes unexpectedly. Check whether you turned the tile over instead of rotating it on the work surface. The British Origami Society explains that turning paper over also changes how a fold is viewed: a mountain can be worked as a valley from the opposite face. See Valley & Mountain folds.

The rotated element no longer fits. Compare its displayed width and height with the available backing area. Use a larger square backing or remake the elements to a smaller common size. Avoid correcting only one tile if that would make its border visibly different.

The ridges point correctly but stop awkwardly at a seam. Orientation and alignment are separate decisions. Either reposition the elements to align their crease ends or use consistent borders so each tile reads as an individual textured unit.

One tile looks denser than the others. Compare crease spacing first, then the amount each accordion is opened. Adjust the opening if the folds match; remake the element if its crease spacing differs substantially.

Finish by checking the complete panel against your direction map and confirming that every tile fits its space. Once those decisions are settled, attach the remaining pieces in sequence, preserving the pleat opening and border established by your first completed tile.

• Valley & Mountain folds — British Origami Society, text and artwork by Nick Robinson
• Origami Tessellation Terms and Definitions — Madonna Yoder, Gathering Folds
• Tiling-Based Origami Tessellation Design — Madonna Yoder, Gathering Folds