Modular Origami Unit Count Calculator

Modular origami builds complex 3D structures by interlocking many identical folded paper units. The number of units required depends on the underlying polyhedron and the unit type.

Unit Counts by Polyhedron

Most popular models:

• Sonobe Cube: 6 units (simplest modular model)
• Sonobe Stellated Octahedron: 12 units (most popular beginner project)
• Sonobe Icosahedron: 30 units (beautiful star ball)
• Kusudama (flower ball): Typically 12–60 units depending on design
• Buckyball (truncated icosahedron): 90 units

How big will it actually be?

This is where most unit-count calculators wave their hands, and the answer is not a single scale factor. A 6-unit cube and a 120-unit rhombicosidodecahedron folded from the same paper are wildly different sizes, because the units go on the edges of the underlying solid and a solid with more edges is simply bigger.

Two steps get you there.

Step one: paper to edge length. A Sonobe unit folded from a square of side p produces an assembled edge of

edge = p / (2√2) ≈ 0.354 × p

You can check that against a model on your desk. Six units from 15 cm kami give a cube 5.3 cm on a side, and 15 / 2.828 = 5.30.

Step two: edge length to overall size. Every uniform polyhedron has a fixed ratio between its circumradius R and its edge a, so the span across the finished ball is 2 × (R/a) × edge:

The 90-unit buckyball from the same sheet is nearly three times the width of the cube. That is the number people are surprised by, and it is why buying paper for a buckyball at your usual size gives you something the size of a football.

Spikes add more. Most Sonobe balls are stellated, meaning a pyramid sits on every face. Those points stick out past the circumradius, so add roughly a quarter again to the span. The classic 30-unit Sonobe ball from 15 cm paper measures around 13 cm tip to tip rather than the 10.1 cm of the bare icosahedron underneath it.

Kusudama are a different animal. The units are petals glued or sewn into flowers rather than edges of a polyhedron, so the old rule of thumb applies instead: diameter roughly equal to the paper size, a little over for a 60-unit ball and a little under for a 12-unit one.

Paper Quantity Planning

Always prepare extra units (5–10% more) for mistakes or units that do not fold crisply enough. For color patterns:

Colors for Even Distribution:

• 6 units: 1, 2, 3, or 6 colors
• 12 units: 1, 2, 3, 4, 6, or 12 colors
• 30 units: 1, 2, 3, 5, 6, 10, 15, or 30 colors
• The most visually appealing patterns use 3, 5, or 6 colors

Worked Example

Sonobe icosahedron in 5 colors:

• Units needed: 30
• Units per color: 30 / 5 = 6 each
• Extra (10%): 3 spare = 33 total sheets
• Paper size: 6 × 6 inches
• Edge length: 6 / 2.828 = 2.12 inches
• Bare icosahedron span: 2 × 0.951 × 2.12 = 4.03 inches
• With the stellation spikes: roughly 5 inches tip to tip

Time Estimate

Folding runs about 1 to 2 minutes per Sonobe unit once you have the sequence, so call it 1.5. Assembly is not a fixed job either: a 6-unit cube snaps together in three minutes, while a 90-unit buckyball takes most of an hour and the last dozen units are the hardest, since the ball is rigid by then and every tab has to be persuaded in. Reckon on roughly a third of the folding time again for assembly.

A 30-unit model works out around an hour all in. Beginners should plan for two or three, and should fold every unit before starting assembly rather than alternating, because your folding gets measurably more consistent after the first ten and consistency is what makes the tabs hold.