An Equal-Area Map Projection For Polyhedral Globes

Numerous polyhedral shapes have been proposed as approximations for globes, and the projection most often used is the Gnomonic, with considerable scale and area distortion. Complicated conformal projections have been designed, but an equal-area projection has been used only once, for the icosahedron. The Lambert Azimuthal Equal-Area projection can be modified to provide an exactly fitting, perfectly equal-area projection for any polyhedral globe that has regular polygons, but is most satisfactory for the dodecahedron with 12 pentagons and for the truncated icosahedron with 20 hexagons and 12 pentagons. On the application to the truncated icosahedron, the angular deformation does not exceed 3.75°, and the scale variation is less than 3.3 percent. These advantages are at the expense of increased interruptions at the polygon edges when the polyhedral globe is unfolded. On a propose de nombreuses formes polyedriques comme approximation de globes et la projection gnomonique est la plus souvent utilisee, avec d...