b. Patent Summary and Claims

The invention relates to cartography.

As the earth is a spherical body, so the only true cartographical representation of its surface must be spherical. All flat surface maps are compromises with truth. For example, Mercator’s projection is true to scale only along the equator, and azimuthal projection is limited to convergence of the meridians at one pole at a time. Other know systems of projection can be made to give uniform scale along parallels, or to give equal areas albeit with exaggerated shape distortions.

Another expedient has been to resolve the earth’s surface into a polyhedron, projecting gnomonically to the facets of the polyhedron, the idea being that the sections of the polyhedron can be assembled on a flat surface to give a truer picture of the earth’s surface and of its directions and distances. Such a system is fettered to the limitations and gross radial distortions which characterize gnomonic projection.

It is an object of my invention to provide a sectional map of the world, or of a portion of its surface, which is so constructed that its parts can be assembled to give a truer overall picture of areas, boundaries, directions and distances than is attainable with any type of plane surface map heretofore known.

Another object has been to provide a subdivision of the earth’s surface for cartographic purposes which will result in sections that can be assembled with fewer sinuses in land areas than is possible with sectional maps heretofore known. Other objects and advantages will appear as the description proceeds.

I have found that by resolving the earth’s surface into sections which are entirely bounded by straight line projections of great circles, and constructing a map on great circle grids, it is possible to maintain a uniform scale peripheral cartographic delineations and to distribute all subsidence distortion from the periphery towards the center. I have discovered further that this system brings the subsidence distortion to an irreducible minimum which, without correction of any kind, is very considerably less than with any system of projection heretofore devised.

Another discovery which I have made is that if the earth’s surface is resolved into six equilateral square sections and eight equilateral triangular sections whose edges match throughout, there is formed a polyhedron all of the vertexes of which lie in great circles of a sphere. this figure I will call a “Dymaxion”. As a consequence, all of the sides of all of the sections are true projections of great circles, and uniform scale peripheral cartographic delineations can be constructed.

R. Buckminster Fuller, “Cartography Patent, 2,393,676”, United States Patent Office, January 29, 1946, p.1, 3


Three Claims:

1. A projected map comprising a plurality of square and triangular sections bearing respectively different map outlines and matching along edges which are representations of projected great circles with uniform scale cartographic delineation along said edges.

2. A map comprising two or more sets of different matching map sections, at least one section of each set being a square and one or more of the others an equilateral triangle, the map on the square sections being constructed on a two-way great circle grid and the map on the triangular sections being constructed on a three-way great circle grid.

3. A map of the world comprising six equilateral square sections and eight equilateral triangular sections matching along edges which are representations of projected great circles with uniform scale cartographic delineations along said edges.

R. Buckminster Fuller, “Cartography Patent, 2,393,676”, United States Patent Office, January 29, 1946, p.1, 3