Waterman butterfly projection

The arrangement is an unfolding of a polyhedral globe with the shape of a truncated octahedron, evoking the butterfly map principle first developed by Bernard J.S.

As Cahill was an architect, his approach tended toward forms that could be demonstrated physically, such as by his flattenable rubber-ball map.

Waterman, on the other hand, derived his design from his work on close-packing of spheres.

To project the sphere to the polyhedron, the Earth is divided into eight octants.

Like Buckminster Fuller's 1943 Dymaxion Projection, an octahedral butterfly map can show all the continents uninterrupted if its octants are divided at a suitable meridian (in this case 20°W) and are joined, for example, at the North Atlantic, as in the 1996 version.