Buckyballs can be thought of as 3-regular polyhedra (or planar graphs, if you will) with only pentagon and hexagon faces, and an easy application of Euler's Formula gives us that the number of pentagons must be exactly 12. We call a Buckyball spherical if the 12 pentagon faces are evenly spaced on the polyhedron. In this talk we will make this definition much more precise and devise a way to classify all spherical Buckyballs. While this result is not new, we believe the approach we use is. Our argument is based on constructing finite, triangular tiles composed of pentagons and hexagons that we map onto the faces of the icosahedron. This process leads us to linear-time algorithms to properly 3-edge color certain classes of spherical Buckyballs. Numerous models will be on hand, and instructions for making one's own Buckyballs out of origami will be made available.
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Cone October 14, 2000