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The Dymaxion map of the Earth is a projection of a global map onto the surface of a polyhedron, which can then be unfolded to a net in many different ways and flattened to form a two-dimensional map which retains most of the relative proportional integrity of the globe map. It was created by Buckminster Fuller, and patented by him in 1946, the patent application showing a projection onto a cuboctahedron. The 1954 version published by Fuller under the title The AirOcean World Map used a slightly modified but mostly regular icosahedron as the base for the projection, and this is the version most commonly referred to today. The name Dymaxion was applied by Fuller to several of his inventions.
Unlike most other projections, the Dymaxion is intended purely for representations of the entire globe. Each face of the polyhedron is a gnomonic projection, so zooming in on one such face renders the Dymaxion equivalent to such a projection.
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Properties
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Fuller claimed his map had several advantages over other projections for world maps.
It has less distortion of relative size of areas, most notably when compared to the Mercator projection; and less distortion of shapes of areas, notably when compared to the Gall-Peters projection. Other compromise projections attempt a similar trade-off.
More unusually, the Dymaxion map has no 'right way up'. Fuller frequently argued that in the universe there is no 'up' and 'down', or 'north' and 'south': only 'in' and 'out'. Gravitational forces of the stars and planets created 'in', meaning 'towards the gravitational center', and 'out', meaning 'away fom the gravitational center'. The north-up-superior/south-down-inferior presentation of most other world maps is linked to cultural bias. Note that there are some other maps that don't put north at the top.
There is no one 'correct' view of the Dymaxion map. Peeling the triangular faces of the icosahedron apart in one way results in an icosahedral net that shows an almost contiguous land mass comprising all of earth's continents - not groups of continents divided by oceans. Peeling the solid apart in a different way presents a view of the world dominated by connected oceans surrounded by land.
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Impact
A 1967 Jasper Johns painting depicts a Dymaxion map. "Map (Based on Buckminster Fuller's Dymaxion Airocean World)" hangs in the permanent collection of the Museum Ludwig in Cologne.
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