How to Flatten and Rotate Waterbomb Nodes in a Paper Tessellation

Waterbomb terminology covers different structures. A conventional waterbomb-base tessellation is a corrugation. Its fully folded configuration differs from the broad, tiled surface you may picture when thinking of a flat tessellation. Helena Verrill explains this distinction in Continuous Deformations of the Waterbomb Base Tessellation, including how related crease patterns can produce other flat-folding forms. Read Verrill’s original paper.

Some waterbomb-style designs do collapse into flagstone arrangements. Eric Gjerde explicitly describes his 3.6.3.6 design as three-dimensional when partly folded and a flagstone tessellation when fully folded. In a separate example, he describes waterbombed shapes becoming twists as their peaks collapse. These examples establish a useful possibility, but they do not make every waterbomb peak interchangeable with a twist. Gjerde’s crease-pattern explanation and his waterbomb-to-twist example.

Before adjusting the paper, compare your model with the designer’s finished front and back views. Establish whether your target is a compressed corrugation, a flat arrangement of overlapping twists, or a deliberately raised surface. Use that target throughout the following steps.

Keep the crease pattern and its mountain-and-valley key beside the model. A mountain crease forms a ridge on the face you are viewing; a valley crease forms a trough. Turning the sheet over reverses their appearance, so choose one reference face before checking assignments.

Start with a node whose creases you can see clearly, preferably near an accessible edge. Partially reopen the adjoining units until you can distinguish individual layers. Leave enough movement for the connecting folds to open and close while you work.

Treat this as a diagnostic workflow derived from the source geometry, rather than a replacement for a particular designer’s folding sequence. Verrill notes that a crease pattern alone does not specify how far each crease closes or how the layers overlap. A finished photograph or folding sequence supplies information the line drawing may omit. Why a crease pattern does not fully specify the folded form.

Check these three things before pressing anything firmly:

• Each crease meets the intended intersection rather than a nearby accidental crease.
• Mountain and valley assignments match the pattern from your chosen reference face.
• Connecting folds have room to move beyond the node you are holding.

If the basic collapse is unfamiliar, rehearse it on a separate square. Jasper’s waterbomb-base instructions establish horizontal and vertical creases, turn the sheet over to establish the diagonals, and then bring opposite sides inward so the layers settle into a triangular base with four flaps. This demonstrates coordinated folding around a central intersection. Folding Diagrams for the Waterbomb Base.

An embedded tessellation node remains attached to its neighbors, so use your actual pattern’s assignments rather than transferring every crease from the practice square. The rehearsal teaches the closing motion; the tessellation determines which folds participate.

For the working node, use this sequence:

1. Partially open the raised area so its existing creases are visible.
2. Support the surrounding paper loosely between your fingers.
3. Encourage the designated valleys inward while allowing the mountain ridges to rise.
4. Bring the participating layers toward one another in small increments.
5. Pause before full compression and inspect both faces for a trapped flap.

The useful checkpoint is an orderly partial collapse: the layers follow existing creases, and you can reopen the unit without introducing another fold. If a panel bows across its middle, reopen the area and inspect the adjacent crease assignments before continuing.

For this task, “rotating a node” means guiding the paper around the central intersection into its intended layered arrangement. The movement occurs through the surrounding folds. In twist-compatible waterbomb designs, the collapsed shape can become a twist, as Gjerde’s documented example shows. Waterbomb shapes becoming twists.

Keep the unit partly open while establishing its direction. Hold the surrounding sheet loosely with one hand and guide the emerging folded shape with the other. Follow the direction shown in the designer’s sequence or the orientation of an equivalent completed unit. As you turn it slightly, allow each connecting fold to adjust before turning farther.

Judge the movement by the paper’s behavior. A promising direction lets the specified creases close while the faces between them remain orderly. If the turn requires a new diagonal, traps a flap, or pulls an adjoining unit out of its intended arrangement, return to the last open position and check the pattern.

Avoid assigning a quarter-turn or half-turn simply because the visible unit is square or triangular. Establish the endpoint from the intended layer arrangement. Also keep the viewing face consistent: a turn described as clockwise from the front appears counterclockwise from the back.

When no rotation is shown and the unit closes correctly as a waterbomb corrugation, continue that collapse. Introducing a twist would be a change to the design.

Once the unit reaches its intended orientation, lower the remaining raised folds gradually. Support the underside and guide each flap into its shown overlap before applying firm pressure. Inspect the reverse face again; an apparently neat front can conceal a flap folded across the wrong line.

Use fingertips to set the creases after the layers are arranged. If a bulky spot remains, reopen it enough to identify the layer causing it. Flattening is the finishing stage of the collapse, so resolve the geometry before trying to compress the stack.

Move to a neighboring unit while leaving the connection between them partly open. Resolve its folds, then revisit the first unit to check that both still match the intended pattern. This two-unit check is a practical way to catch an incompatible overlap before repeating it across a row.

Gjerde notes that his 3.6.3.6 waterbomb/flagstone design requires considerable pinching and shaping to collapse. He also states that the published pattern omits some small hourglass creases. If you are using that specific drawing, those omissions matter: the drawing alone is not a complete beginner folding sequence. Designer’s notes on collapse and omitted creases.

Use the location of the obstruction to decide what to reopen. The following checks are practical inferences from crease assignments, layer overlap, and connections between units; they are not measurements from a folding experiment.

What you observe	What to inspect	Next action
One panel develops a new bend	Its bounding creases and the nearest intersection	Reopen the panel and restore the specified folds.
The node turns, but a neighboring unit lifts	The shared connection and both units’ overlaps	Loosen both units and resolve them together.
The front looks finished but the reverse has a protruding flap	The underside layer order	Reopen locally and place the flap as shown in the finished model.
The unit closes neatly but remains a narrow corrugation	The intended finished form	Confirm whether that compressed form is the design’s endpoint.
Several units stop at the same stage	Pattern completeness and the folding sequence	Check for omitted shaping folds or an intermediate step.

A node that closes successfully by itself still needs to work with its neighbors. Likewise, a raised section is not automatically an error. Compare the whole small patch with the intended finished form before changing a crease assignment.

A useful finishing check has three parts: the unit has the intended orientation, its layers follow the intended overlap, and the adjacent units can reach their own finished positions. Look across both faces rather than judging only the central peak.

Complete one small patch before extending the same method across the sheet. Establish the collapse, guide any designed rotation, inspect the underside, and only then set the folds. That sequence gives you a repeatable way to flatten compatible waterbomb nodes while preserving the structure of the tessellation.

• Continuous Deformations of the Waterbomb Base Tessellation — H. A. Verrill
• Folding Diagrams for the Prayer Fold and Waterbomb Base — Jasper
• 3.6.3.6 Waterbomb / Flagstone Tessellation, Crease Pattern — Eric Gjerde
• Kites, Waterbomb / Flagstone Tessellation, WIP — Eric Gjerde