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### What is meant by 'no visual distortion'?

When transferring geographic data from the globe onto a flat plane, distortions will always occur in either shape, size, area, distance or direction.

On projections such as the Mercator map, the further north of south of the equator one goes, the more extreme the distortion becomes. When comparing the Mercator map to a globe, it is easy for everyone to see that Greenland, for example, is much larger on the flat Mercator map than it is on the globe.

However, when visually comparing land masses on Fuller's map to that of a globe, the land masses appear to have their correct size.

The Peters projection, on the other hand, sacrifices shape to preserve relative accuracy in overall land area; distortions are obvious when comparing it to the globe. However, there are no visible shape discrepancies in any of the land masses on Fuller's map when it is compared to a globe.

Minute area and shape distortions can be detected mathematically and are equally distributed throughout the map. Visually, however, these distortions are negligible.

### Why an icosahedron?

A polyhedron is a many-sided 3-dimensional object. An icosahedron is a polyhedron with 20 equilateral triangular faces. Of the five Platonic polyhedra (all of which have equal faces in size and shape), the icosahedron most closely approximates a sphere.

Fuller found that the best way to lay various polyhedra flat while keeping all the land masses unbroken was to use the icosahedron. With only two exceptions, all the breaks needed to lay the icosahedron flat occur completely within the oceans, and, therefore, keeps the division of land masses to a minimum.

With minor adjustments to two triangular faces, Fuller's Dymaxion Air-Ocean World Map provides us with a flat view of all the Earth's land masses 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 skin out flat. Notice how it needs breaks, or 'sinuses' in many different places in order to lay flat. The more breaks introduced, the flatter the orange peel will lay.

When an icosahedron is unfolded and laid flat, breaks need to be introduced, just as in the case of the orange peel. The question is then where to introduce these breaks? One way of doing this is to introduce the breaks in the oceans as much as possible. This provides a world view in which the land masses are unbroken.

Fuller's map was actually designed to have all of the icosahedron's triangles separable. This allowed the map to be dynamic. By rearranging the triangles, with the South Pole at the center of the map, navigation routes by sea become readily apparent, just as air routes across the North Pole are obvious in the original configuration.

Fuller explored more than 25 different useful configurations of the Dymaxion Air-Ocean World Map. Each configuration introduces breaks in different places and allows different aspects of the world to be emphasized.

### Why are the mean low temperature zones shown?

The Fuller Projection defines our world not in terms of political boundaries or physical features but by temperature zone. Buckminster Fuller was interested in the history of human migration and the geographical areas of technological innovation as it related to temperature.

Looking at the yellow band closest to the North Pole we find that the mean low temperature ranges from 23 degrees to 41 degrees Fahrenheit. Fuller found that throughout history, humans migrated east to west along the 32 degree freezing line and that the majority of the dominant centers of modern civilization can be found to lie somewhere within this optimum temperature band. He felt that social patterns, human preoccupations and economic customs are determined by how cold it gets, not by how hot.

Buckminster Fuller then realized that: (I ) the colder an area gets the larger the fluctuation in temperature is to be found, and (2) the more a geographical area's temperature varies, the more technologically inventive must humans living there become in order to survive. (For example, they must learn to build boats to cross a lake in summer, as well as design sleds to cross the ice in winter.)

### Fuller's Projection Method

Fuller superimposed a spherical icosahedron grid onto the Earth's sphere. Each of the grid's edges are arcs of "Great Circles" which show the shortest routes between two points on a sphere's surface.

When the Great Circle arcs are unfolded, the arc-edges of the spherical icosahedron become the straight edges of the regular icosahedron and the twenty spherical triangles become twenty plane triangles. Since the arc-edges are unfolded, their lengths remain undistorted. Minute distortion in the middle of each triangle is distributed evenly throughout the map.

The Fuller Projection is not a 'shadow' projection as most maps are because the world is not projected' onto a regular icosahedron but rather unfolds into an icosahedron. Thus, Fuller preferred to call his map a "transformation". During this transformation, the line from the sphere's center through the sphere's surface and out to the zenith point is kept at a constant 90 degree angle with respect to the map's surface. Fuller referred to this as a "constant zenith projection."

Buckminster Fuller Institute

Updated: 2007/06/29

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