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This Science Lab activity provides instructions and materials for building a paper model of a fullerene. You can download a PDF file of the experiment which may be duplicated and distributed to your students.

C 60 molecule

Each person or team working on the model will also need two copies of each of 2 patterns. You may download PDF files for printing of Pattern 1 and Pattern 2.
The fullerene is in the shape of a truncated icosahedron. This shape is familiar to many people as a football, or soccer ball if you are in the USA. (Truncating An Icosahedron describes how this is done.)
The truncated icosahedron is one of 13 semi-regular polyhedra that are known as the Archimedean solids*. Each semi-regular polyhedron is made up of faces that are two or more different kinds of regular polygons. In this case, there are 20 hexagons and 12 pentagons. In our paper model the pentagons are open space, each surrounded by 5 hexagons. There are also five regular polyhedra, known as the Platonic solids, which consist of faces that are all the same regular polygon. One of these is a cube, with 6 square faces. Another is the tetrahedron, which has four triangular faces.

Cubane molecule

A fuller discussion of the geometry of these solids may be found in Mathematics: A Human Endeavor by Harold R. Jacobs, published by W.H. Freeman and Company, San Francisco.
The fullerene is not the only molecule in the shape of an Archimedean or Platonic solid. Cubane (C₈H₈) consists of 8 carbon atoms arranged at the vertices of a cube with a hydrogen atom bonded to each carbon.

Phosphorus molecule

The hydrogens are at the vertices of a larger cube.
White phosphorus (P₄) consists of four phosphorus atoms arranged at the vertices of a tetrahedron.

Dodecahedrane molecule

Dodecahedrane (C₂₀H₂₀) is in the shape of a dodecahedron. This is the 12-sided solid that is sometimes used to make desk calendars with each month on one of the 12 pentagon shaped faces. The Dodecahedrane molecule has a carbon atom at each of the 20 vertices of the dodecahedron, with a hydrogen atom attached to each carbon.
For other interesting molecules visit the Molecule of the Month web site.
 
*They are named after Archimedes, the guy who is best known for overflowing his bathtub to discover the principle of buoyancy. See the Buoyancy Experiment for more