THE FULLER PROJECTION Dymaxion™ Air-Ocean World

dynamic + maximum + tension=Doing More With Less

A map of the Earth which presents geographic information in a single, comprehensive picture without breaks in any of the continental contours, or any visible distortion of the relative shapesor sizes of the landmasses.

A world projection with negligible distortionwhich can accurately display at-a-glanceglobal information such as human migrationpatterns and the distribution of natural resources.

A New Perception of EarthWorld maps are symbolic tools which help to shape our perception of the Earth. Every world map projec-tion must make certain compromisesas information is transferred from aspherical globe to a flat surface. With this in mind, as early as 1927Buckminster Fuller, an educator, engi-neer, architect, author, cartographerand futurist, set out to develop theworld’s most accurate 2-dimensionalworld map. He wanted to provide aview of the whole Earth at oncewhich would have the ability to revealmajor trends in world affairs andshow the shortest air routes betweenland masses. Fuller predicted eventhen that global travel would shiftfrom the sea to the sky and anticipat-ed the emergence of what he termed “a One-Town Air-Ocean World.”

Designing for AccuracyIt took almost a quarter of a centuryfor Fuller to fine-tune the mathemat-ics that could render an accurate view of Earth as a flat world map. Whileperfecting his “great circle” mappingtechniques, Fuller first published his final icosahedral version of the map in 1954. Using the form of an icosahedron, a polyhedron with 20 triangular faces, Fuller was able to accurately depict the whole earth on a flat map with only the tiniest bitof distortion, not even visible to thehuman eye, distributed among the triangles uniformly. The outer edges of each triangle display the informa-tion with absolute accuracy.

Fuller called his final map projectionthe “Dymaxion Air-Ocean World.” (the term “Dymaxion” was coined in the 1930’s from Fuller’s most commonly used words, dynamic, maximum and tension.) In the late1970s, Fuller’s associates, Robert Grip

and Christopher Kitrick added to the accuracy of the Dymaxion Map byusing computer generated algorithmsfor latitude and longitude information.

A Tool for Global ResponsibilityWith our increasing global awareness, a world map is needed which enablesus to highlight the relationshipsamong all nations and cultures of theworld. Environmental concerns arebecoming a central focus of our inter-national agenda. Therefore, we mustlearn to see what unites us ratherthan what separates us and to chartglobal resources, population and dis-tribution patterns which characterizethe complex trends and critical needs of the world today. In Fuller’s ownwords, the Dymaxion Map reveals a One-World Island at the bottom of an “air-ocean” which helps us to view the world as one interdependentsystem of relationships.

What is meant by no visual distortion?’All flat world map projections contain a considerable amount of distortion either in shape, area, distance or direction. For instance, on a standard Mercator world map projection, Greenland is three times its normal size and Antarctica appearsas a long thin strip of land. Even thepopular Robinson Projection, an elliptical map that was officiallyadopted as National Geographic’s standard in 1988 and now used inmost schools, still contains a largeamount of distortion—with Greenland60 percent larger than it really is. The Peters projection, on the otherhand, sacrafices shape to preserve relative accuracy in overall land area,distortions which are obvious whencomparing it to the globe. However,there are no visible shape discrepanciesin any of the landmasses on Fuller’smap when it is compared to a globe.Minute area and shape distortions canbe detected mathematically and areequally distributed throughout themap. Visually, however, these distor-tions are negligible.

Why an icosahedron?A polyhedron is a many-sided 3-dimentional object. An icosahedronis a polyhedron with 20 triangularfaces. Of the five Platonic polyhedra(all of which have equal faces in sizeand shape), the icosahedron mostclosely approximates a sphere. Fuller

found that the best way to lay variouspolyhedra flat while keeping all thelandmasses unbroken was to use theicosahedron. With only two exceptions,all the breaks needed to lay the icosa-hedron flat occur completely withinthe oceans, and, therefore, keep thedivision of the land masses to a mini-mum. With minor adjustments to twotriangular faces, Fuller’s Dymaxion™Air-Ocean World Map provides us with a flat view of all the Earth’s landmasses as unbroken islands in a single world ocean.

Why are the oceans broken up?Try peeling an orange while keeping the skin in one piece. Then lay the skinout flat. Notice how it needs breaks, or “sinuses” in many different places in order to lay flat. The more breaksintroduced, the flatter the orange peelwill lay. When an icosahedron isunfolded and laid flat, breaks need tobe introduced, just as in the case ofthe orange peel. The question is thenwhere to introduce these breaks? One way of doing this is to introducethe breaks in the ocean as much apossible. This provides a world-view inwhich the landmasses are unbroken.

Fuller’s map was actuallydesigned to have all of the icosahe-dron ’s triangles separable. Thisallowed the map to be dynamic. Byrearranging the triangles, with theSouth Pole at the center of the map,navigation routes by sea became readi-ly apparent, just as air routes across

the North Pole are obvious in the originalconfiguration. Fuller explored morethan 25 different useful configurationsof the Dymaxion™ Air-Ocean WorldMap. Each configuration introducesbreaks in different places and allows different aspects of the world to beemphasized.

Fuller’s Projection Method

Fuller superimposed a sphericalicosahedron grid onto the Earth’ssphere. Each of the grid’s edges arearcs of “Great Circles” ●a whichshow the shortest routes betweentwo points on a sphere’s surface.

When the Great Circle arcs areunfolded, the arc-edges of thespherical icosahedron become the straight edges of the regularicosahedron ●b and the twentyspherical triangles become twentyplane triangles. ●c

Since the arc-edges are unfolded,their lengths remain undistorted.Minute distortion in the middle of each triangle is distributedevenly throughout the map. ●dFuller referred to his map as “a constant zenith projection.”

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Commonly asked questions about the Fuller Projection

For more info contact: The Buckminster Fuller Institute111 N. Main StreetSebastopol, California 95472800-967-6277 www.bfi.orgwww.spaceshipearth.org

©2002 Buckminster Fuller Institute. The word Dymaxion and the Dymaxion Mapdesign are trademarks of The BuckminsterFuller Institute. The map is also copyrightedby the Buckminster Fuller Institute, 1938,1967, 1980 + 1992.

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