TheDymaxion map projection, also called theFuller projection, is a kind ofpolyhedral map projection of the Earth's surface onto the unfoldednet of anicosahedron. The resulting map is heavilyinterrupted in order to reduce shape and size distortion compared to otherworld maps, but the interruptions are chosen to lie in the ocean.
The projection was invented byBuckminster Fuller. In 1943, Fuller proposed a projection onto acuboctahedron, which he called theDymaxion World, using the nameDymaxion which he also applied to several of his other inventions. In 1954, Fuller and cartographerShoji Sadao produced an updated Dymaxion map, theAirocean World Map, based on an icosahedron with a few of the triangular faces cut to avoid breaks in landmasses.
The Dymaxion projection is intended for representations of the entire Earth.
The March 1, 1943, edition ofLife magazine included a photographic essay titled "Life Presents R. Buckminster Fuller's Dymaxion World", illustrating a projection onto acuboctahedron, including several examples of possible arrangements of the square and triangular pieces, and a pull-out section of one-sided magazine pages with the map faces printed on them, intended to be cut out and glued to card stock to make a three-dimensional cuboctahedron or its two-dimensional net.[1] Fuller applied for a patent in the United States in February 1944 for the cuboctahedron projection, which was issued in January 1946.[2]
In 1954, Fuller and cartographerShoji Sadao produced a new map onto an icosahedron instead of the cuboctahedron. It depicts Earth's continents as "one island", or nearlycontiguous land masses. References today to the Fuller projection or Dymaxion usually indicate this version.
Unlike otherpolyhedral map projections, the Dymaxion map does not use agnomonic projection (perspective projection through the Earth's center onto the polyhedral surface), which causes length distortion away from the center of each face. Instead each triangle's three edges on the Dymaxion map match the scale along the corresponding arcs ofgreat circles on the Earth (modeled as a sphere), and then the scale diminishes toward the middle of the triangle.[3] The transformation process was formally mathematically defined in 1978.[4][5][6][7]
Though neitherconformal norequal-area,[8] Fuller claimed that 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 theMercator projection; and less distortion of shapes of areas, notably when compared to theGall–Peters projection. Othercompromise projections attempt a similar trade-off.
More unusually, the Dymaxion map does not have any "right way up". Fuller argued that in the universe there is no "up" and "down", or "north" and "south": only "in" and "out".[9] Gravitational forces of the stars and planets created "in", meaning "towards the gravitational center", and "out", meaning "away from the gravitational center". He attributed the north-up-superior/south-down-inferior presentation of most other world maps tocultural bias.
Fuller intended the map to be unfolded in different ways to emphasize different aspects of the world.[10] 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.
Showing the continents as "one island earth" also helped Fuller explain, in his bookCritical Path, the journeys of early seafaring people, who were in effect usingprevailing winds to circumnavigate this world island.
However, the Dymaxion map can also prove difficult to use. It is, for example, confusing to describe the fourcardinal directions and locategeographic coordinates. The awkward shape of the map may be counterintuitive to most people trying to use it. For example, the shortest route from Africa to South America is not obvious. Depending on how the map is projected, land masses and oceans are often divided into several pieces.
In 2019, Daniel "daan" Strebe developed aconformal icosahedral projection, similar to the conformal projections to an octahedron byOscar S. Adams (1928) and to a tetrahedron byLaurence P. Lee (1965), all three usingDixon elliptic functions. A conformal map preserves angles and local shapes from the sphere at the expense of increasing the scale distortion near the vertices of the icosahedron.[11]
Fuller projection
Dymaxion-like conformal projectionComparison of the Fuller projection and Strebe's Dymaxion-like
conformal projection withTissot's indicatrices at 30° intervals
A 1967Jasper Johns painting,Map (Based on Buckminster Fuller's Dymaxion Airocean World), depicting a Dymaxion map, hangs in the permanent collection of theMuseum Ludwig inCologne.[12][13]
TheWorld Game, a collaborative simulation game in which players attempt to solve world problems,[14][15] is played on a 70-by-35-foot Dymaxion map.[16]
In 2013, to commemorate the 70th anniversary of the publication of the Dymaxion map inLife magazine, the Buckminster Fuller Institute announced the "Dymax Redux", a competition for graphic designers and visual artists to re-imagine the Dymaxion map.[17][18] The competition received over 300 entries from 42 countries.[17]
The H3 hierarchicalglobal grid implemented byUber uses an icosahedron oriented in Dymaxion orientation, then further subdivided into hexagons.[19]
In 2020, a collaborative effort by thousands ofMinecraft players, theBuild the Earth project, used Strebe's conformal variant as a projection for building a 1:1 scale representation of the Earth inside the game.[20]
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