Abstract
Robert Gray has derived exact transformation equations for Buckminster Fuller's icosahedron-based world map projection. This paper presents three alternative sets of transformation equations for the same map projection: one based on spherical linear interpolation, another using intersections of geodesics, and the third using spherical triangles. Further, the exact solution is given here for the inverse transformation equation stated, but not solved, by Gray. This solution leads to various inverse procedures for Fuller's map projection.
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