A "Slice-and-Dice" Approach to Area Equivalence in Polyhedral Map Projections

Abstract

For centuries, people have been intrigued by map projections upon polyhedra—the surface of the Earth laid out on the faces of polyhedral bodies (beautiful in themselves)—which are then unfolded to make flat maps of the world. This paper describes a simple "slice-and-dice" method to obtain area equivalence, which is applied to polyhedral globes. The implementations of this method include a projection that is equivalent to Snyder's equal-area projection for Platonic bodies, an equal-area projection with far smaller cusps, and an equal-area projection that obtains constant scale along the polyhedron's edges. The latter two are presented in terms of exact equations and are compared with Snyder's projection.