Dymaxion Map

Fuller's icosahedral world-map projection—foldable, with no fixed "up," showing Earth's continents as "one island."

The Dymaxion map, also called the Fuller map, projects the world onto the surface of an icosahedron that can be unfolded and flattened into two dimensions. Its faces are interrupted at the edges so as to preserve the shapes and sizes of land masses. Fuller first presented the idea in the March 1, 1943, issue of Life magazine—"Life Presents R. Buckminster Fuller's Dymaxion World"—which included a cut-out readers could assemble into a rough globe or lay flat. Fuller filed a U.S. patent in 1944 (issued 1946) showing a projection onto a cuboctahedron. In 1954 Fuller and cartographer Shoji Sadao produced the refined Airocean World Map on a regular icosahedron, the version most often reproduced today.

Though neither conformal nor equal-area, the Dymaxion map achieves relatively low distortion of both size and shape compared with the Mercator or Gall–Peters projections. Its most distinctive property is that it has no single "right way up." Fuller argued that the universe has no absolute up or down, only "in" and "out" relative to gravitational centers, and he attributed the conventional north-up orientation of maps to cultural bias. The projection is designed only for whole-globe representations; unlike a gnomonic projection, each triangular edge matches the scale of a great circle while interior points shrink toward the facet's middle.

Because the icosahedron can be peeled apart in different ways, the same map can emphasize different truths: one unfolding shows the continents as a nearly contiguous "one island Earth," another shows the world's oceans as one connected body surrounded by land. In Critical Path Fuller used the "one island" view to explain the wind-driven voyages of early seafaring peoples. The map's drawbacks are equally real—cardinal directions and coordinates are awkward, and the shortest route between two points is often not obvious. Its cultural reach is wide: Jasper Johns based his 1967 painting Map on it, and the World Game is played on a 70-by-35-foot Dymaxion floor map. Later mathematicians derived exact transformation equations, and in 2019 Daniel Strebe produced a conformal variant.

See Also

• R. Buckminster Fuller (R. Buckminster Fuller) — the central figure
• Shoji Sadao (link) — co-produced the Airocean World Map
• Jasper Johns (link) — based his 1967 painting Map on it
• World Game Institute (link) — the simulation played on a Dymaxion map

Sources

• Dymaxion map (Wikipedia)