Modular Origami Unit Count Calculator
Calculate the number of paper units needed for modular origami polyhedra like Sonobe, Kusudama, and other models.
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
| Polyhedron | Faces | Edges | Units (Edge-based) | Units (Face-based) |
|---|---|---|---|---|
| Tetrahedron | 4 | 6 | 6 | 4 |
| Cube | 6 | 12 | 12 | 6 |
| Octahedron | 8 | 12 | 12 | 8 |
| Icosahedron | 20 | 30 | 30 | 20 |
| Dodecahedron | 12 | 30 | 30 | 12 |
| Truncated Icosahedron | 32 | 90 | 90 | 32 |
| Rhombicosidodecahedron | 62 | 120 | 120 | 62 |
| Stellated Octahedron | 8 | 12 | 12 | — |
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
Paper Size Formula
The finished model size is proportional to the paper size used:
Finished Diameter ≈ Paper Size × Scale Factor
| Unit Type | Scale Factor | Notes |
|---|---|---|
| Sonobe | 0.7–0.8 | From edge length |
| Kusudama (5-petal) | 1.0–1.2 | Diameter relative to paper |
| PHiZZ unit | 0.6–0.7 | Tom Hull’s design |
For a 6-inch paper making a 30-unit Sonobe icosahedron: finished diameter ≈ 6 × 0.75 = 4.5 inches.
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
- Finished size: ~4.5 inches diameter
Time Estimate
An experienced folder takes about 1–2 minutes per Sonobe unit, plus 10–20 minutes for assembly. A 30-unit model takes roughly 45–80 minutes total. Beginners should plan for 2–3 hours.