1. A computer-implemented method for projecting geographic data from a spherical surface to a two-dimensional Cartesian space, comprising: projecting the geographic data from the spherical surface onto faces of a three-dimensional polyhedron; arranging the faces of the three-dimensional polyhedron within the two-dimensional Cartesian space according to a cutout pattern corresponding to a shape of the three-dimensional polyhedron, wherein geographic data points associated with the spherical surface are mapped to a first set of Cartesian coordinates associated with the arranged faces within two-dimensional Cartesian space; and mapping one or more data points in the geographic data points to a second set of Cartesian coordinates outside of the cutout pattern and within the two-dimensional Cartesian space based on the arranging so that relative distances among the geographic data points remain consistent between the spherical surface and the two-dimensional Cartesian space.