| Abstract: | Part of a cuboctahedron-based geodesic map projection by Buckminster Fuller is expanded to spherical quadrilaterals with opposite sides equal. Points on such a quadrilateral can be described by intersections of geodesics, which provide parameterized coordinate values in a Geodesic Coordinate System. Through a linear transform of the geodesic coordinates, a spherical quadrilateral maps to a parallelogram. The resulting map has the same constant scale on all four sides. Within the map, all lines parallel to the sides correspond to geodesics on the globe. Spherical rectangles, spherical squares, and diamonds (spherical rhombi) are specifically examined; various tiling sets of diamonds can be used to cover the globe. Non-projection applications in geometry, astronomy, and computer graphics are described. |
