World Game™ Workshop

Making maps of the world has been a problem ever since we discovered that the Earth is not flat.  A globe is spherical and can be used to represent the world accurately but it provides a limited view; we cannot study the whole of the Earth’s surface at the same time. Transferring data from a sphere to a flat surface presents great difficulties and always results in some distortion. In the commonly seen Mercator projection, invented in the sixteenth century, a cylinder is placed around the globe so that the two surfaces touch along the equator. The features on the surface of the sphere are then projected outwards until they meet the cylinder. The map is an exact representation along the line of contact, but away from the equator the map is less precise. The distortion is worse near the poles; the poles themselves cannot be represented.

Buckminster Fuller was frustrated by this inaccurate view of the world in which Greenland appears three times as large as South America when, in reality, the opposite is the case. Distortion must occur in any flat maps of the Earth but it might be possible to smear it out evenly so that it is less noticeable. Fuller sought to show that the shape distribution and relative sizes of the Earth’s landmasses while containing the worst distortion to the seventy-five percent of the Earth’s surface covered by water.

He took a regular solid, the icosahedron, composed of twenty equilateral triangles and subdivided each face into smaller triangles. Calculating from a similar grid superimposed on the Earth he could transfer the data from the sphere to the polyhedron. This was all done between the two world wars before computers were available to assist with the calculations. The resulting map is unique in its lack of visible distortions. Fuller also had to choose the position of the icosahedron carefully so that it could be cut along its edges and opened out flat without creating unnatural breaks in any landmass. The result known as the Dymaxion Map™ is shown in the accompanying figure.

 In February 1943, Life magazine included a colour, cut-out version of Fuller’s map. Before it was published, the editors had the map examined by a panel of experts to certify that it was an accurate representation of the Earth and that it was a new discovery. The panel which included the Chief Geographer of the U.S. State department and two mathematicians, could not find geographical or mathematical flaws in Fuller’s map but were still uncertain as to how it had been created. In terms filled with negative connotations, their report concluded that it was ‘pure invention’. When Fuller applied for a patent on his map he found a ruling had been issued which decreed all possible projection methods used in cartography had been exhausted.  Hence his application was rejected.  He presented the Patent Office with the Life report. The testimony of the experts could not be argued with and he was granted the first patent [in the twentieth] century for innovation in map-making.

Peter R. Cromwell | Polyhedra | Cambridge University Press | 1997

Fuller was a prominent modernist, architect and industrial designer who wanted to produce a map of the world with no significant distortions to any of the major land masses. The Dymaxion™ projection does this though it produces a world that, at first, may seem disorienting.  This is not necessarily such a bad thing, for it can force us to take a fresh look at the world and at the relationships between places. Because Europe, North America and Japan are all located toward the center of this map projection, it is particularly useful  for illustrating two of the central themes of this book: the relationships among these prosperous regions, and the relationships between this prosperous group and the less prosperous countries of the world. On Fuller’s projection, the economically peripheral countries of the world are shown being cartographically peripheral too. 

Sallie A. Marston | Paul L. Knox | Diana M. Liverman | World Regions: People, Places and Environments | Prentice Hall | 2002