Modular Origami

Every model in Origami and Paper Folding 1 to 6 came from a single sheet. Modular origami breaks that rule on purpose. You fold several identical pieces, called units, and lock them together without glue. Each unit is simple, so the skill shifts from clever folding to being accurate and repeating the same fold many times. The reward is models that would be impossible from one square: cubes, stars and balls with many points.

How Units Lock Together

A modular unit has two kinds of feature. A pocket is a fold of paper with an opening, and a tab (or flap) is a point that slides into a pocket. When every unit has tabs and pockets in matching places, units grip each other by friction, and the finished model holds itself together.

• Identical units. Most modular models use one unit, repeated. Making them all the same is what makes the result symmetrical.
• Colour as a design tool. Using three or four colours in a fixed pattern turns a plain model into a decorated one, with no extra folding.
• Small squares work well. Squares of 7.5 cm (a 15 cm square cut in four) are easy to hold and give a model that fits on the palm.

The Sonobe Unit

The sonobe is the best-known modular unit. It makes a shallow parallelogram with two tabs and two pockets. Fold one carefully, then check it against the description below before making more.

1. Start with a square, coloured side down. Fold it in half and unfold, leaving a centre crease.
2. Fold both long edges to the centre crease, then unfold them. You now have three equal creases across the square.
3. Turn the paper over. Fold the lower left corner up and the upper right corner down so that each corner's edge lines up with the nearest quarter crease, forming two small triangles on opposite ends.
4. Fold the long edges back in to the centre crease, folding over the triangles. This gives a long parallelogram.
5. Fold the two triangular points over along the line where they meet the strip, so each end of the strip is tucked into a neat triangle.
6. Fold the unit in half along the centre crease and open it slightly. You should see two triangular tabs at the ends and two pockets running along the inside.

The Models

The same unit builds different models. The only thing that changes is how many units you use and how you connect them.

Model 1: The Cube

The cube uses six units, one for each face. It is the best first assembly, because the six units are all equal and the result shows at once whether your units are accurate.

1. Choose colours. Fold two units in each of three colours, so opposite faces match.
2. Join two units. Slide a tab of one unit into a pocket of another. The two units now form a corner.
3. Add a third unit into the corner so that all three tabs are used. This makes a cube corner with three faces meeting.
4. Add the remaining three units one at a time, tucking each tab into the nearest free pocket. Do not push them fully home until all six are in place.
5. Tighten. Once all six units are connected, push each tab firmly into its pocket and square up the edges. The cube holds its own shape.

Model 2: The Star

The star uses thirty units and is the classic larger sonobe project. It looks like a ball covered in points, and the colour pattern matters more here than anywhere: use five colours, and place each colour on six units, spaced evenly around the model.

1. Fold 30 units, six in each of five colours. Count them as you go, because the model needs exactly thirty.
2. Build a ring of units that form a star-shaped section, with the points all facing out.
3. Add rings row by row, connecting each unit to the units beside it and below it.
4. Close the model by connecting the last ring. You should find that the final units fit without forcing; if they do not, an earlier connection is loose.

Counting Units

Modular models need exact counts, and mistakes show up late, when you run out of one colour. A small script helps you plan how many units of each colour to fold for a model:

Output when run:

Assembling and Keeping Tension

A modular model is held together by friction, so its strength comes from how well the units fit. Most failures come from a few causes, all of them easy to fix.

• Do not force it early. Join all the units loosely first, then tighten them in a second pass. Forcing the first connections leaves later ones too tight to fit.
• Choose paper that grips. Paper that is too thin does not grip and too thick does not fold. Standard origami paper or light card is about right.
• Crease firmly. A sharp crease in each tab and pocket is what makes a connection hold.
• Add a dab of glue only as a last resort. A pure modular model should hold without it, and a model that does is a mark of accurate folding.

Challenges

Each challenge has a worked solution you can open after you have tried it.

Next, in Origami and Paper Folding 8, we look at tessellations and patterns: repeating crease patterns, twist folds, and the idea of a crease pattern as a map.