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."Fuller applied for a patent in the United States in February 1944, the patent application showing a projection onto a cuboctahedron. The patent was issued in January 1946.
The 1954 version published by Fuller, made with co-cartographer Shoji Sadao, the Airocean World Map, used a modified but mostly regular icosahedron as the base for the projection, which is the version most commonly referred to today. This version depicts the 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.
The name Dymaxion was applied by Fuller to several of his inventions.
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".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.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, tracing a path from India to Chile may be confusing. Depending on how the map is projected, land masses and oceans are often divided into several pieces.
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.
The World Game, a collaborative simulation game in which players attempt to solve world problems,is played on a 70-by-35-foot Dymaxion map.
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.The competition received over 300 entries from 42 countries.
Richard Buckminster Fuller was an American architect, systems theorist, author, designer, inventor, and futurist. Fuller published more than 30 books, coining or popularizing terms such as "Spaceship Earth", "Dymaxion", ephemeralization, synergetic, and "tensegrity". He also developed numerous inventions, mainly architectural designs, and popularized the widely known geodesic dome. Carbon molecules known as fullerenes were later named by scientists for their structural and mathematical resemblance to geodesic spheres.
In geometry, a cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertices, with 2 triangles and 2 squares meeting at each, and 24 identical edges, each separating a triangle from a square. As such, it is a quasiregular polyhedron, i.e. an Archimedean solid that is not only vertex-transitive but also edge-transitive. It is the only radially equilateral convex polyhedron.
In geometry, a regular icosahedron is a convex polyhedron with 20 faces, 30 edges and 12 vertices. It is one of the five Platonic solids, and the one with the most sides.
A map is a symbolic depiction emphasizing relationships between elements of some space, such as objects, regions, or themes.
In geometry, the truncated icosahedron is an Archimedean solid, one of 13 convex isogonal nonprismatic solids whose 32 faces are two or more types of regular polygons.
In cartography, a map projection is a way to flatten a globe's surface into a plane in order to make a map. This requires a systematic transformation of the latitudes and longitudes of locations from the surface of the globe into locations on a plane. All projections of a sphere on a plane necessarily distort the surface in some way and to some extent. Depending on the purpose of the map, some distortions are acceptable and others are not; therefore, different map projections exist in order to preserve some properties of the sphere-like body at the expense of other properties. Every distinct map projection distorts in a distinct way, by definition. The study of map projections is the characterization of these distortions. There is no limit to the number of possible map projections. Projections are a subject of several pure mathematical fields, including differential geometry, projective geometry, and manifolds. However, "map projection" refers specifically to a cartographic projection.
A geodesic dome is a hemispherical thin-shell structure (lattice-shell) based on a geodesic polyhedron. The triangular elements of the dome are structurally rigid and distribute the structural stress throughout the structure, making geodesic domes able to withstand very heavy loads for their size.
Tensegrity, tensional integrity or floating compression is a structural principle based on a system of isolated components under compression inside a network of continuous tension, and arranged in such a way that the compressed members do not touch each other while the prestressed tensioned members delineate the system spatially.
The Dymaxion House was developed by inventor and architect Buckminster Fuller to address several perceived shortcomings with existing homebuilding techniques. Fuller designed several versions of the house at different times — all of them factory manufactured kits, assembled on site, intended to be suitable for any site or environment and to use resources efficiently. A key design consideration of the design was ease of shipment and assembly.
The Dymaxion car was designed by American inventor Buckminster Fuller during the Great Depression and featured prominently at Chicago's 1933/1934 World's Fair. Fuller built three experimental prototypes with naval architect Starling Burgess – using donated money as well as a family inheritance – to explore not an automobile per se, but the 'ground-taxiing phase' of a vehicle that might one day be designed to fly, land and drive – an "Omni-Medium Transport". Fuller associated the word Dymaxion with much of his work, a portmanteau of the words dynamic, maximum, and tension, to summarize his goal to do more with less.
World Game, sometimes called the World Peace Game, is an educational simulation developed by Buckminster Fuller in 1961 to help create solutions to overpopulation and the uneven distribution of global resources. This alternative to war games uses Fuller's Dymaxion map and requires a group of players to cooperatively solve a set of metaphorical scenarios, thus challenging the dominant nation-state perspective with a more holistic "total world" view. The idea was to "make the world work for 100% of humanity in the shortest possible time through spontaneous cooperation without ecological damage or disadvantage to anyone," thus increasing the quality of life for all people.
A world map is a map of most or all of the surface of Earth. World maps form a distinctive category of maps due to the problem of projection. Maps by necessity distort the presentation of the earth's surface. These distortions reach extremes in a world map. The many ways of projecting the earth reflect diverse technical and aesthetic goals for world maps.
The Mollweide projection is an equal-area, pseudocylindrical map projection generally used for global maps of the world or night sky. It is also known as the Babinet projection, homalographic projection, homolographic projection, and elliptical projection. The projection trades accuracy of angle and shape for accuracy of proportions in area, and as such is used where that property is needed, such as maps depicting global distributions.
A Gaian is a radical Green who views the ecology of the Earth's biosphere not only as the basis of human moral examples, but of all cognition and even sentience. Advocates of this view claim that since we live as part of one planet's photosynthesis chain and are trapped within its gravity well, we are effectively components of one large body—that being the global ecology of Earth itself.
Bernard Joseph Stanislaus Cahill, American cartographer and architect, was the inventor of the octahedral "Butterfly Map". An early proponent of the San Francisco Civic Center, he also designed hotels, factories and mausoleums like the Columbarium of San Francisco.
The Waterman "Butterfly" World Map is a map arrangement created by Steve Waterman. Waterman first published a map in this arrangement in 1996. The arrangement is an unfolding of a globe treated as a truncated octahedron, evoking the butterfly map principle first developed by Bernard J.S. Cahill (1866–1944) in 1909. Cahill and Waterman maps can be shown in various profiles, typically linked at the north Pacific or north Atlantic oceans.
The Cahill–Keyes projection is a polyhedral compromise map projection first proposed by Gene Keyes in 1975. The projection is a refinement of an earlier 1909 projection by Cahill. The projection was designed to achieve a number of desirable characteristics, namely symmetry of component maps (octants), scalability allowing the map to continue to work well even at high resolution, uniformity of geocells, metric-based joining edges, minimized distortion compared to a globe, and an easily understood orientation to enhance general usability and teachability.
AuthaGraph is an approximately equal-area world map projection invented by Japanese architect Hajime Narukawa in 1999. The map is made by equally dividing a spherical surface into 96 triangles, transferring it to a tetrahedron while maintaining area proportions, and unfolding it onto a rectangle. The map substantially preserves sizes and shapes of all continents and oceans while it reduces distortions of their shapes, as inspired by the Dymaxion map. The projection does not have some of the major distortions of the Mercator projection, like the expansion of countries in far northern latitudes, and allows for Antarctica to be displayed accurately and in whole. Triangular world maps are also possible using the same method. The name is derived from "authalic" and "graph".
Hajime Narukawa is a Japanese architect. He was born in 1971 in Kawasaki-City, Kanagawa and lives and practices in Tokyo.
In map projections, an interruption is any place where the globe has been split. All map projections are interrupted at at least one point. Typical world maps are interrupted along an entire meridian. In that typical case, the interruption forms an east/west boundary, even though the globe has no boundaries.
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