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