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Cahill 1909

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

CONTENTS
Click inside boxes to open other sections in separate windows.

1) Introduction and Background Notes	2) 1943: Cubo-Octahedron, Split Continents	3) 1944: Cubo-Octahedron, Whole Continents
4) 1946: The Dymaxion Map Patent	5) 1954 Icosahedron, 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.

Then 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:

	Fuller	Cahill
1	Asymmetry of layout; also has two split triangles	Octants in perfect symmetry
2	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
3	Contortion of Korea and Norway	No distortion of Korea and Norway
4	Poor scalability; the larger the map the worse it looks	Good at any scale from smallest to largest
5	Anti-metric, irrational, unstated edges of facets: 7,048.89 km	Octant edges are 10,000 km: basis of metric system
6	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
7	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.