In the 1943 Buckminster
Fuller developed a projection of the world on a cubo-octahedron, which
he published in Life Magazine. He issued a revised version on
an icosahedron in 1954. In 1980 his associates developed a more accurate
representation using 20 equilateral triangles.
“There are problems with projecting a spherical surface
onto a plane. The zenithal projection preserves distances from the
zenith at the expense of only being able to show half the world or
less. Mercator's projection preserves shapes but distorts relative
size. Peter's projection does the opposite. Gall's projection is a
kind of compromise between the two. Hammer's projection preserves
relative areas but the distortions at its edge are more extreme than
with Gall's, and the latitude lines are not parallel.
“There are also interrupted projections, like
Mollweide's, which preserve parallel latitudes but forbid continuous
planar depiction, as the term suggests. This means that sea and air
routes cannot be clearly shown if land masses are left intact. The
oblique Aitoff projection keeps areas equal and is uninterrupted, but
land-masses at the map's edge seem unclear.
“Fuller's projection is interrupted but provides for
sectional rearrangement to emphasize differing geographical
relationships. There is little distortion of shape or size, and it
employs a geodesic grid reference. It also provides universal
viewpoint: Earth's centre and the zenith are always perpendicularly
below and above each point."