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A brief overview of R. Buckminster Fuller's world maps is presented. Exact transformation equations for Fuller's icosahedron-based world map are derived. These equations are differentiable and therefore suitable for standard area distortion analysis. Such distortion analysis has been carried out, and the results are compared to the familiar gnomonic projection onto an icosahedron. In addition to the exact forward unit sphere to XY-plane transformation equations, a relation in one parameter, which must be satisfied by the inverse transformation, is given.
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Robert W. Gray (1995) studied this question.
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