Dymaxion map

The Dymaxion map or Fuller map is a projection of a world map onto the surface of an icosahedron, which can be unfolded and flattened to two dimensions. The flat map is heavily interrupted in order to preserve shapes and sizes. The projection was invented by Buckminster Fuller. The March 1, 1943, edition of Life magazine included a photographic essay titled "Life Presents R. Buckminster Fuller's Dymaxion World". The article included several examples of its use together with a pull-out section th…

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Jump to content Main menu Main menu move to sidebar hide Navigation Main page Contents Current events Random article About Wikipedia Contact us Contribute Help Learn to edit Community portal Recent changes Upload file Special pages Search Search Appearance Donate Create account Log in Personal tools Donate Create account Log in Contents move to sidebar hide (Top) 1 Properties 2 Impact 3 See also 4 References 5 External links Toggle the table of contents Dymaxion map 18 languages Català Ελληνικά Español Euskara Français עברית हिन्दी Magyar Bahasa Indonesia Italiano 日本語 Nederlands Norsk nynorsk Português Русский Svenska Українська 中文 Edit links Article Talk English Read Edit View history Tools Tools move to sidebar hide Actions Read Edit View history General What links here Related changes Upload file Permanent link Page information Cite this page Get shortened URL Print/export Download as PDF Printable version In other projects Wikimedia Commons Wikidata item Appearance move to sidebar hide From Wikipedia, the free encyclopedia This is an old revision of this page, as edited by InternetArchiveBot ( talk | contribs ) at 20:36, 10 August 2023 (Rescuing 1 sources and tagging 0 as dead.) #IABot (v2.0.9.5) ( Whoop whoop pull up - 14403) . The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision . Revision as of 20:36, 10 August 2023 by InternetArchiveBot ( talk | contribs ) (Rescuing 1 sources and tagging 0 as dead.) #IABot (v2.0.9.5) ( Whoop whoop pull up - 14403) ( diff ) ← Previous revision | Latest revision ( diff ) | Newer revision → ( diff ) Polyhedral compromise map projection The world on a Dymaxion projection, with 15° graticule Dymaxion projection with Tissot's indicatrix of deformation An icosahedron, the shape the world map is projected onto before unfolding The world flattens to a Dymaxion map as it unfolds into an icosahedron net with nearly contiguous land masses. This icosahedral net shows connected oceans surrounding Antarctica . Example of use illustrating early human migrations according to mitochondrial population genetics (numbers are millennia before present) Dymaxion map of the world with the 30 largest countries and territories by total area , roughly to scale The Dymaxion map or Fuller map is a projection of a world map onto the surface of an icosahedron , which can be unfolded and flattened to two dimensions. The flat map is heavily interrupted in order to preserve shapes and sizes. The projection was invented by Buckminster Fuller . The March 1, 1943, edition of Life magazine included a photographic essay titled "Life Presents R. Buckminster Fuller's Dymaxion World". The article included several examples of its use together with a pull-out section that could be assembled as a "three-dimensional approximation of a globe or laid out as a flat map, with which the world may be fitted together and rearranged to illuminate special aspects of its geography". 1 Fuller applied for a patent in the United States in February 1944, showing a projection onto a cuboctahedron , which he called "dymaxion". The patent was issued in January 1946. 2 In 1954, Fuller and cartographer Shoji Sadao produced the Airocean World Map , a version of the Dymaxion map that used a modified but mostly regular icosahedron as the base for the projection. The version most commonly referred to today, it depicts Earth's continents as "one island", or nearly contiguous land masses. The Dymaxion projection is intended only for representations of the entire globe. It is not a gnomonic projection , whereby global data expands from the center point of a tangent facet outward to the edges. Instead, each triangle edge of the Dymaxion map matches the scale of a partial great circle on a corresponding globe, and other points within each facet shrink toward its middle, rather than enlarging to the peripheries. 3 Fuller's 1980 version of the Dymaxion map was the first definition and use of a mathematical transformation process to make the map. 4 5 6 7 It is a polyhedral map projection . The name Dymaxion was applied by Fuller to several of his inventions. Properties Though neither conformal nor equal-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 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 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 to cultural 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 book Critical Path , the journeys of early seafaring people, who were in effect using prevailing winds to circumnavigate this world island. However, the Dymaxion map can also prove difficult to use. It is, for example, confusing to describe the four cardinal directions and locate geographic 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. Impact A 1967 Jasper Johns painting, Map (Based on Buckminster Fuller's Dymaxion Airocean World) , depicting a Dymaxion map, hangs in the permanent collection of the Museum Ludwig in Cologne . 11 12 The World Game , a collaborative simulation game in which players attempt to solve world problems, 13 14 is played on a 70-by-35-foot Dymaxion map. 15 In 2013, to commemorate the 70th anniversary of the publication of the Dymaxion map in Life magazine, the Buckminster Fuller Institute announced the "Dymax Redux", a competition for graphic designers and visual artists to re-imagine the Dymaxion map. 16 17 The competition received over 300 entries from 42 countries. 16 In 2019, Daniel "daan" Strebe used mathematical work on conformal projections by Oscar S. Adams and L. P. Lee to create a conformal version of the Dymaxion projection. 18 In 2020, the Build the Earth project used Strebe's work to create a map projection for their work known as the Modified Airocean. This map projection provides an extremely low amount of distortion of both shapes and sizes on land, at the cost of heavily distorting the oceans. Unlike the Dymaxion, Modified Airocean is not intended to be unfolded into a 3D object like an icosahedron, and has its continents placed such that it looks somewhat similar to an equirectangular projection . 19 Fuller projection Dymaxion-like conformal projection Comparison of the Fuller projection and Strebe's Dymaxion-like conformal projection with Tissot's indicatrices at 30° intervals See also List of map projections Authagraph projection , inspired by Fuller, 1999 Peirce quincuncial projection , 1879 Polyhedral map projection , earliest known is by Leonardo da Vinci, 1514 References ^ "Life Presents R. Buckminster Fuller's Dymaxion World" . LIFE . 1 March 1943. pp. 41– 55. ^ U.S. patent 2,393,676 ^ Fuller, Ideas and Integrities (1969 ed., p. 139). ^ Gray, Robert W. (1994-01-01). "Fuller's Dymaxion Map" . Cartography and Geographic Information Systems . 21 (4): 243– 246. doi : 10.1559/152304094782540628 (inactive 1 August 2023). ISSN 1050-9844 . {{ cite journal }} : CS1 maint: DOI inactive as of August 2023 ( link ) ^ Gray, Robert W. (1995-10-01). "Exact Transformation Equations for Fuller's World Map" . Cartographica: The International Journal for Geographic Information and Geovisualization . 32 (3): 17– 25. doi : 10.3138/1677-3273-Q862-1885 . ISSN 0317-7173 . ^ Crider, John E. (2008-03-01). "Exact Equations for Fuller's Map Projection and Inverse" . Cartographica: The International Journal for Geographic Information and Geovisualization . 43 (1): 67– 72. doi : 10.3138/carto.43.1.67 . ISSN 0317-7173 . ^ "Dymaxion Map Transformations - Technical White Paper" , Kitrick, Christopher, 2018 ^ "Fuller—ArcGIS Pro | Documentation" . ^ Fuller, Intuition (1972). ^ "Frequently Asked Questions About The Fuller Projection" , Buckminster Fuller Institute, 1992, accessed 2010-07-28 ^ "Kulturelles Erbe Köln: Johns, Jasper, Map (Weltkarte)" . www.kulturelles-erbe-koeln.de . Retrieved 2017-01-18 . ^ "Ausstellung "Ludwig goes Pop" " . ^ Richards, Allen (May–June 1971). "R. Buckminster Fuller: Designer of the Geodesic Dome and the World Game" . Mother Earth News . Retrieved 19 January 2014 . ^ Aigner, Hal (November–December 1970). "Sustaining Planet Earth: Researching World Resources" . Mother Earth News . Retrieved 19 January 2014 . ^ Perry, Tony (October 2, 1995). "This Game Anything but Child's Play : Buckminster Fuller's creation aims to fight the real enemies of mankind: starvation, disease and illiteracy" . The Los Angeles Times . Retrieved 19 January 2014 . ^ a b "DYMAX REDUX Winner" . The Buckminster Fuller Institute. Archived from the original on 2 February 2014 . Retrieved 21 January 2014 . ^ Campbell-Dollaghan, Kelsey (July 22, 2013). "7 Brilliant Reinventions of Buckminster Fuller's Dymaxion Map" . Gizmodo . Retrieved 21 January 2014 . ^ Strebe, Daniel. "Directory of Map Projections: dymaxion-like conformal" . Mapthematics . Mapthematics LLC . Retrieved 2022-06-19 . ^ Archived at Ghostarchive and the Wayback Machine : We are now ready to Build The Earth, 1:1 scale in Minecraft , retrieved 2021-04-01 External links Wikimedia Commons has media related to Fuller projection . Fuller Map homepage Dymaxion Project Animation Icosahedron and Fuller maps Dynamically generated maps based on the Dymaxion projection v t e Map projection History List Portal By surface Cylindrical Mercator -conformal Gauss–Krüger Transverse Mercator Oblique Mercator Equal-area Balthasart Behrmann Gall–Peters Hobo–Dyer Lambert Smyth equal-surface Trystan Edwards Cassini Central Equirectangular Gall stereographic Gall isographic Miller Space-oblique Mercator Web Mercator Pseudocylindrical Equal-area Collignon Eckert II Eckert IV Eckert VI Equal Earth Goode homolosine Mollweide Sinusoidal Tobler hyperelliptical Kavrayskiy VII Wagner VI Winkel I and II Conical Albers Equidistant Lambert conformal Pseudoconical Bonne Bottomley Polyconic American Chinese Werner Azimuthal (planar) General perspective Gnomonic Orthographic Stereographic Equidistant Lambert equal-area Pseudoazimuthal Aitoff Hammer Wiechel Winkel tripel By metric Conformal Adams hemisphere-in-a-square Gauss–Krüger Guyou hemisphere-in-a-square Lambert conformal conic Mercator Peirce quincuncial Stereographic Transverse Mercator Equal-area Bonne Sinusoidal Werner Bottomley Sinusoidal Werner Cylindrical Balthasart Behrmann Gall–Peters Hobo–Dyer Lambert cylindrical equal-area Smyth equal-surface Trystan Edwards Tobler hyperelliptical Collignon Mollweide Albers Briesemeister Eckert II Eckert IV Eckert VI Equal Earth Goode homolosine Hammer Lambert azimuthal equal-area Quadrilateralized spherical cube Strebe 1995 Equidistant in some aspect Conic Equirectangular Sinusoidal Two-point Werner Gnomonic Gnomonic Loxodromic Loximuthal Mercator Retroazimuthal (Mecca or Qibla) Craig Hammer Littrow By construction Compromise Chamberlin trimetric Kavrayskiy VII Miller cylindrical Natural Earth Robinson Van der Grinten Wagner VI Winkel tripel Hybrid Goode homolosine HEALPix Perspective Planar Gnomonic Orthographic Stereographic Central cylindrical Polyhedral AuthaGraph Cahill Butterfly Cahill–Keyes M-shape Dymaxion ISEA Quadrilateralized spherical cube Waterman butterfly See also Interruption (map projection) Latitude Longitude Tissot's indicatrix Map projection of the tri-axial ellipsoid v t e Buckminster Fuller Books Nine Chains to the Moon (1938) Operating Manual for Spaceship Earth (1968) Critical Path (1981) Dymaxion Chronofile Other Dymaxion house (1928) Dymaxion car (1933) Dymaxion deployment unit (1940) Dymaxion map (1946) Tensegrity (1949) Geodesic dome (1953) World Game (1961) Octet truss (1961) Fly's Eye Dome (1965) Expo 67 United States Pavilion (1967) Related Allegra Fuller Snyder (daughter) Current solar income Synergetics Design science revolution Design science Cloud Nine tensegrity sphere Energy slave Geoscope Dymaxion Proposed Brooklyn Dodgers stadium Gold Dome Old Man River's City project R. Buckminster Fuller and Anne Hewlett Dome Home Ephemeralization Fullerene Buckminsterfullerene Buckminster Fuller Challenge Buckminster Fuller: Thinking Out Loud (1996 documentary) The Last Dymaxion: Buckminster Fuller's Dream Restored (2012 documentary) Karlis Johansons Kenneth Snelson Category Commons Authority control databases International FAST National United States Israel Retrieved from " https://en.wikipedia.org/w/index.php?title=Dymaxion_map&oldid=1169715041 " Categories : CS1 maint: DOI inactive as of August 2023 Buckminster Fuller Map projections 1943 introductions Hidden categories: Articles with short description Short description is different from Wikidata Commons category link is on Wikidata This page was last edited on 10 August 2023, at 20:36 (UTC) . This version of the page has been revised . Besides normal editing, the reason for revision may have been that this version contains factual inaccuracies, vandalism, outdated information, or material not compatible with the Creative Commons Attribution-ShareAlike 4.0 License . Privacy policy About Wikipedia Disclaimers Contact Wikipedia Legal & safety contacts Code of Conduct Developers Statistics Cookie statement Mobile view Search Search Toggle the table of contents Dymaxion map 18 languages Add topic