Compound Polyhedra - Modular Origami

Origami experts know that understanding shape and geometry is vital. Building complex shapes from paper is still not simple. Mathematics at school or college rarely prepares us for such a practical task.

Modular origami for the tetrahedron, the octahedron and beyond

Modular origami answers that challenge: each model is assembled from many identical folded units. This unit origami method lets each module lock into its neighbours, so the paper builds compound polyhedra that a single sheet could not.

Fergus Currie's book of geometric models in advanced modular origami gives full instructions and origami diagrams for elegant, beautiful and practical models, such as:

• The Compound of Two Cubes
• The Compound of Two Tetrahedra
• The Compound of the Octahedron and the Cube
• The Compound of Three Cubes
• The Compound of Five Octahedra
• The Compound of Three Octahedra
• The Compound of Three Tetrahedra
• The Compound of the Icosahedron and the Dodecahedron
• The Small Triambic Icosahedron (STI)
• The Compound of the STI and the Dodecahedron

The maths behind the icosahedron and dodecahedron models

The book also has an introduction with sections on the mathematical ideas behind the models and a short history of modular origami. You can see how the triangular faces of the octahedron interlock with a cube, or how the dodecahedron's pentagonal faces sit within an icosahedron. Both solids are linked to the golden ratio: the twelve vertices of an icosahedron lie on three golden rectangles.

A section on tools and folding techniques prepares you before the first fold. A gallery of the finished models in the book shows you each target before you start.

Building modular origami polyhedra: a practical, systematic guide

Constructing such complex origami structures is not easy, so the book is written for patient folders. Tarquin has over 50 years of experience in papercraft, origami and mathematics for young and old. Printed in full colour, the book is practical and systematic: you work step by step towards modular origami models that are striking to display.

Beyond compounds: the cuboctahedron and truncated octahedron

Most origami polyhedra start from square paper folded into one repeated module. The Sonobe unit is the classic example: six of them lock together into a cube.

Other systems use stem units, where each folded strip becomes an edge, or an open frame unit that leaves the faces hollow. The difference lies in what you see: solid faces, or the skeleton of the solid.

A natural next step after compounds is the Archimedean solids. The cuboctahedron mixes squares and triangles, while the truncated tetrahedron and truncated octahedron bring in hexagonal faces. The truncated cube swaps the squares of a cube for octagons, with a small triangle at each corner.

The rhombicuboctahedron, icosidodecahedron and buckyball

The rhombicuboctahedron has 8 triangles and 18 squares, and the icosidodecahedron 20 triangles and 12 pentagons. The buckyball, or truncated icosahedron, combines 12 pentagons with 20 hexagons, like a football. These modular origami polyhedra suit folders who have already built a tetrahedron or a cube and want a larger count of units.

From the octahedron to the dodecahedron: understanding through geometric origami

Origami mastery depends on understanding complex shapes. With Fergus Currie's help, exploring compound polyhedra through geometric origami builds that understanding fold by fold. In practice, a good first project is the Compound of Two Cubes, before you move on to five interlocking octahedra.

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