Exact Transformation Equations for Fuller's World Map

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. Les equations de transformation exacte pour la carte du monde de Fuller On presente un bref survol des cartes du monde de R. Buckminster Fuller. On derive ensuite les equations de transformation exacte pour la carte du monde de Fuller basee sur un icosaedre. Ces equations sont differentielles et conviennent donc a l'analyse normale de distortion des aires. Une telle analyse a ete effectuee et l'on compare les resultats a la projection gnomonique familiere...