Go back to B.J.S. Cahill Resource Page
Cahill Butterfly Map 1909
Cahill 1909
Go back to Gene Keyes home page

Cahill-Keyes M-layout world map silhouette including Antarctica
Cahill-Keyes 1975
Why Cahill? What about Buckminster Fuller?

Evolution of the Dymaxion Map:
An Illustrated Tour and Critique

Part 1

by Gene Keyes

Summary: I love Bucky, but Cahill's map is a lot better. Here's how.

Click inside boxes to open other sections in separate windows.
1) Introduction and
Background Notes
2) 1943:
Split Continents

3) 1944:
Whole Continents

4) 1946:
The Dymaxion Map Patent

5) 1954
Whole Continents

6) 1967 ff:
Later Editions and
World Game Versions

7) 1995 ff
Dymaxion Maps
on the Internet

8) Notes on Scaling Dymaxion Maps
9) Critique:
Dymaxion Map Compared to Cahill

Part 1
Introduction and Background Notes

Since 1961 I have been a devotee and student of R. Buckminster Fuller (1895-1983): the noted geodesic dome inventer, architect, designer, futurist, philosopher, and great helmsman of Spaceship Earth. In particular his "Dymaxion World Map" had caught my attention back then for its feat of showing all continents uninterrupted and with minimal distortion.

When I resumed college studies in 1969, I chose Southern Illinois University, Carbondale, in part because it was home base to Fuller, who was loosely affiliated with its Design Department. (Most of the time Bucky was lecturing elsewhere around the world.) I participated in early versions of his "World Game", and created a Special Major of "Government: War-Peace Studies" to include Fuller's perspective in my world politics curriculum. (Hat tip to H.F.W. "Bill" Perk, my teacher there, who carried on Fuller's legacy at SIU.)

For the World Game, we used wall-size outline versions of the Dymaxion Map, ca. 1 m x 2 m, (over 3' x 6'); 1/20,700,000. I  acquired some more of those and others, and went on to study them in minute detail.

In 1973 my (international relations) M.A. thesis at Southern Illinois University was entitled "Six Principles for a Unified Map System (Applied to the China-Russia Situation)" (213 p. + 49 maps). In it, I not only celebrated the Fuller projection, but also adopted it as the base map for the System being proposed in that thesis.

I discovered B.J.S.Cahill's 1909 Octahedral Butterfly World Map: and found, after a lot more study, that Cahill had already accomplished Fuller's whole-earth map principles, a lot earlier, and with much greater elegance. Cahill had all the continents unbroken, and with minimal distortion, in a design of perfect symmetry, interchangeable with a globe.

I elaborated that appraisal in a 46-page paper in 1975, entitled "World Maps, World Politics, and World Vision." as part of my Ph.D. Comprehensive Exams at York University in Toronto. It was accepted for publication in an International Studies Association journal International Studies Notes [now defunct], but then the editor reneged; and lost the manuscript and its original illustrations. (I still have the Xeroxes.) Meanwhile, I had to focus on my dissertation (1975-1978), and temporary positions as Assistant Professor of Political Science at Brandon University (1978-80) and St. Thomas University (1982-83).

I made a nine-day visit to Cahill's archives in 1983; and until 1984 did a lot more work on Cahill. I also computed and executed a re-design of Cahill's octahedral map (modestly named "Cahill-Keyes"), with certain improvements, and adapting Fuller's projection concept into it. But exigencies arose which put the project in mothballs until my recent retirement, and launching of this website.

The 46-page essay needs to be updated. Meanwhile, I am posting its precis in the appendix below to provide a context for my critique of Buckminster Fuller's Dymaxion World Map, as compared to B.J.S. Cahill's Octahedral World Map. My purpose here is not to diminish Fuller, but to show that if Cahill had already made a better map than such a visionary as Bucky, it is a feather in Cahill's cap, not a demerit for the Dymaxion. Fuller's map was a milestone toward the invention of the geodesic dome: achievement enough. But his map is a poor teaching tool which does not match well with a globe, and that is where Cahill succeeds.

In this presentation, besides showing the Dymaxion map in all its stages since 1943, I will fault it on the following points, none of which afflict Cahill:

Asymmetry of layout; also has two split triangles
Octants in perfect symmetry
Irregularity of graticule; different grid in every facet; meridians and parallels splayed and bent; low-resolution 15° geocells
Identical grid in every facet, smooth curves and meridians; suitable for high resolution 5° or 1° geocells
Contortion of Korea and Norway
No distortion of Korea and Norway
Poor scalability; the larger the map the worse it looks
Good at any scale from smallest to largest
Anti-metric, irrational, unstated edges of facets: 7,048.89 km
Octant edges are 10,000 km: basis of metric system
Poor fidelity to globe: off-center icosahedron not aligned, nor in scale, to any meridian or parallel; no comparable 5° geocells
Perfect visual fidelity to globe; octants aligned to axis, poles,  equator, and all parallels and meridians; has 5° geocells
Poor learnability: 22 disorienting facets; no equivalent spherical icosadron-globe
Global teaching tool par excellence in eight easy pieces; Cahill map is globe's alter ego

In particular, I will be emphasizing the importance of a 1° or at least 5° graticule (latitude-longitude grid) for world maps and globes, because this provides the most direct basis of comparison between map and globe. Fuller’s coarse 15° graticule hides its flaws; whereas Cahill’s map looks fine at any degree of resolution.

Fig. 1.1 below: Here is a rare example of a world map with a 5° grid — in fact, two maps: a Mercator, and an orthographic globe. Unfortunately, the grid does not go onto the land masses, nor farther toward the poles on the Mercator, only reaching 75° N or S.
Mercator & Orthographic 5 degree maps

Source: http://content.answers.com/main/content/img/
   [delete line-space-break if using URL]
Enlarged to 105% by Gene Keyes to 1/200,000,000.

A century ago, in 1909, Cahill was among the first to denounce the Mercator map for its widespread mis-use in schools and in general — a mockery of its navigational purpose. But even today in the Internet age, Mercator and its ilk continue their merry way, mis-informing minds everywhere. Just to take one example:  all Google maps begin with Mercator. What . . . !

Map-design-seekers are often asked: for what purpose do you want to use it? The conventional wisdom is that you must go with many different projections. Cahill begged to differ, and I concur:

I want a single, general purpose, world map projection, with high fidelity to a globe, suitable at all scales from smallest to largest, good for one country or the whole planet. I want a world map and globe as a synoptic pair, comparable to each other at a glance, or in detail. I want geography learners at any age to be able to grasp the globe and world map as readily as do-re-mi.

By these criteria, Fuller falters; Cahill excels.


Gene Keyes
Political Science Department, York University, Toronto

[Cover page:]


An Appreciation of B.J.S. Cahill (1866-1944)

plus remarks on

William Archer
R. Buckminster Fuller
John Paul Goode

The human intellect, organizing, order-bringing, must enlarge itself so as to embrace, in one great conspectus, the problems, not of a parish, or a nation, but of the pendant globe.
     --William Archer, 1912

The creation of a master plan of the world is a matter of design first and foremost, the design of a frame within which intensive mathematical details shall be afterwards subordinated.
     --B.J.S. Cahill, 1928

My task as inventor is to employ the earth's resources and energy income in such a way as to support all humanity while also enabling all people to enjoy the whole earth, all its historical artificts and its beautiful places without one man interfering with the other, and without any man enjoying life around the earth at the cost of another.
     --R. Buckminster Fuller, 1966

Cahill's projection of the world is undubitably the right one . . .
     --Ambrose Bierce, ca. 1912

[Precis, slightly revised 2009-06-01]

Part I reports the dismal results of map tests I gave in a world politics class. The students' warped awareness of simple geography is symptomatic of the grossly distorted world maps to which we are all constantly exposed, and which this paper condemns as one cause of ubiquitous geopolitical ignorance. Especially deplorable are Mercator, and Goode's Homolosine.

Part II is an appraisal of B.J.S. Cahill (1866-1944) as a neglected genius of world map design. His elegant octahedronal "Butterfly" map (1909 et seq) refuted the myth that a plane surface cannot show a reasonable likeness of the continents as on a globe. J.P. Goode (1862-1932) praised the Cahill map, but later (1923) produced a travesty, the now commonplace Homolosine. This paper analyzes the Cahill world map, and traces its history, early acclaim, and ultimate eclipse by misbegotten rivals. It renews Cahill's unmet challenge to judge the map against any alternative.

One such is Buckminster Fuller's 1943/1954 "Dymaxion" map, a noteworthy but awkward design. Although strongly influenced by.Fuller's worldview and mapwork, this paper lauds the felicity of the Cahill model over Fuller's, using seven criteria: symmetry; graticular regularity; non-distortion of Korea; scalability; metric measurement; fidelity to globe; and teaching-tool learnability.

Part III discusses the stultifying effects on world order thinking caused by anachronistic maps, mostly Eurocentric peepholes, or open-ended Goode aberrations and Mercator absurdities. It cites the Sprouts, Fuller, Cahill, and others, and quotes from a long-forgotten 1912 book by William Archer, The Great Analysis: A Plea for Rational World Order which is a whole-earth manifesto so prophetic it could have been written next week. The import of Cahill's map is that, even better than Fuller's, it can foster a corrected, balanced, and closed-system image of the total planet.

The paper concludes by presenting a refined version of the Cahill Butterfly as the basis of a "Coherent World Map System" whose progenitor would be a proposed 1/1,000,000 "Mega-map", a master portrait of the earth in an area 40 meters long (132'). This chart and its derivatives could help renovate geography teaching, and provide a common canvas for world history and world order studies.

Cahill Butterfly Map 1909  

Goode Homolosine Map 1923

Cahill, 1909

Goode, 1923
Fuller icosahedral map 1954
Cahill-Keyes M-layout world map silhouette including Antarctica  
Fuller, 1954
Cahill-Keyes 1975

Source notes:  Cahill (@7 /1/2°; see Part 9.1);

Goode (@20° and 10° at poles) : http://atlas.nrcan.gc.ca/site/english/learningresources/carto_corner/goode.gif

Fuller (@0°): Education Automation, p. 2 (See Part 9.1)

Cahill-Keyes (@5°): drawn and © 1975, 2009 by Gene Keyes

All four reduced to 1/500,000,000 by Gene Keyes

[One of the illustration pages]


4 profiles of USSR & China

Disclaimer: All sources have been credited as best I can; this presentation is a labor-of-love, money-losing hobby, aimed at the increase and diffusion of knowledge; i.e., no  copyrights have been poached for my commercial use, this being a completely non-commercial, non-profit endeavor by a retired professor living on a shoestring.

My own written materials in this llustrated Tour and Critique are freely available under Creative Commons license for fair non-commercial public use. The Cahill-Keyes Map has been copyrighted, but is also freely available for fair non-commercial public use. (All with source-credit, of course!). Just check with me if you have a commercial idea, thanks. 

Though this is not a blog with space for direct posting, I will be happy to include responses, rebuttals, corrections, and comments if you email them to me:

gene.keyes ~~AT~~ gmail.com

as a precaution against gmail's spam-filter, please also send a copy to:

gene.keyes63 ~~AT~~ post.harvard.edu

or snail mail:

Gene Keyes
55 Douglas Ave.
Berwick, Nova Scotia  B0P 1E0

The exposition begins with Fuller's original 1943 Dymaxion map as published in Life magazine.

Go to Part 2
1943: The First Dymaxion Map:
Cubo-Octahedron with Split Continents

Go back to Contents
Go back to B.J.S. Cahill Resource Page

Go back to Gene Keyes home page

Text cc. 2009 by Gene Keyes; Cahill-Keyes Map c. 1975, 2009  by Gene Keyes