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Archimedean Solid Nets

The Archimedean solids have regular faces of two or more kinds, and every corner looks the same: the same faces meet there in the same order. This page has nets for the truncated tetrahedron, the cuboctahedron, the truncated cube, the truncated octahedron, the rhombicuboctahedron, the icosidodecahedron and the truncated icosahedron, whose pentagons and hexagons form the classic soccer ball.

Every net takes up as much of its A4 page as it can, with glue tabs and the finished solid drawn in a corner. With their many faces, these models are best for patient older children and adults.

Part of the Cut-Out Activities collection, Last updated on Thu, 29 Oct 2026 23:45:08 GMT.

Free Printables

Truncated Tetrahedron Net

Truncated tetrahedron net: four hexagons and four triangles, the corners of a tetrahedron cut away.
Truncated tetrahedron net: four hexagons and four triangles, the corners of a tetrahedron cut away. | zuzuzi.com

Cuboctahedron Net

Cuboctahedron net: eight triangles and six squares, two of each meeting at every corner.
Cuboctahedron net: eight triangles and six squares, two of each meeting at every corner. | zuzuzi.com

Truncated Cube Net

Truncated cube net: six octagons and eight small triangles.
Truncated cube net: six octagons and eight small triangles. | zuzuzi.com

Truncated Octahedron Net

Truncated octahedron net: six squares and eight hexagons, a solid that packs with no gaps.
Truncated octahedron net: six squares and eight hexagons, a solid that packs with no gaps. | zuzuzi.com

Rhombicuboctahedron Net

Rhombicuboctahedron net: eighteen squares and eight triangles, three squares and a triangle at each corner.
Rhombicuboctahedron net: eighteen squares and eight triangles, three squares and a triangle at each corner. | zuzuzi.com

Icosidodecahedron Net

Icosidodecahedron net: twenty triangles and twelve pentagons, alternating around every corner.
Icosidodecahedron net: twenty triangles and twelve pentagons, alternating around every corner. | zuzuzi.com

Truncated Icosahedron Net

Truncated icosahedron net: the soccer ball, twelve pentagons and twenty hexagons with glue tabs.
Truncated icosahedron net: the soccer ball, twelve pentagons and twenty hexagons with glue tabs. | zuzuzi.com

Cutting the Corners of a Solid

Several of these shapes come from slicing the corners off a Platonic solid. Cut the corners of a cube and each one leaves a triangle while the squares become octagons: that is the truncated cube. Cut deeper, to the middle of each edge, and you reach the cuboctahedron, with its triangles and squares.

The Soccer Ball Shape

The truncated icosahedron has 12 pentagons and 20 hexagons. Sewn from leather panels and inflated into a sphere, it became the classic soccer ball pattern, and chemists found the same shape in the carbon molecule C60, named buckminsterfullerene.

A Shape That Fills Space

Copies of the truncated octahedron, with its 6 squares and 8 hexagons, can be packed together in space with no gaps at all, just as cubes can. Building a few of them and fitting them together shows it better than any drawing.

Frequently Asked Questions

Why are they named after Archimedes?

Archimedes was a Greek mathematician of the third century BC. A later writer, Pappus of Alexandria, reports that he described thirteen such solids, though his own text is lost. Johannes Kepler studied all thirteen again in 1619.

Which Archimedean net should I start with?

The truncated tetrahedron, with only 8 faces, and the cuboctahedron, with 14, are the gentlest. The rhombicuboctahedron and the icosidodecahedron have more faces, and the truncated icosahedron, with 32 faces and 90 edges, takes the most gluing.