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Constructing a Buckyball with Mathematica: A combination of geometry and algebra from classical and modern mathematics
Author

Michael Trott
Organization: Wolfram Research, Inc.
Department: Scientific Information Group
Description

Instead of using existing polyhedron definitions from standard Mathematica packages, we can use basic algebra operations in Mathematica to construct a buckyball from first principles. One advantage of this is that we can get all the coordinates in the buckyball exactly, rather than as numerical approximations.

We start with the construction of an icosahedron. The vertices of an icosahedron centered at the origin are given by the vertices of three mutually perpendicular rectangles with aspect ratio equal to GoldenRatio.
Subject

*Mathematics > Geometry > Solid Geometry
Keywords

Geometry, Algebra, Golden Ratio, Polygons, Polyhedra, 3D Graphics
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Buckyball.nb (276.6 KB) - Mathematica Notebook