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Cahill Butterfly Map 1909
Cahill 1909
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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 9.1

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

9) Critique: Seven Design Flaws of Fuller's Map as Compared to Cahill's
9.1) Layout assymetrical
9.2) Graticule irregular
9.3) Korea distorted
9.4) Scalability poor
9.5) Anti-metric edges
9.6) Globe fidelity poor
9.7-a) Learnability poor
9.7-b) Learnability poor
9.8) Conclusion

9) Critique
Seven Severe Design Flaws of Fuller's Map
as Compared to Cahill's

Before looking at all the minuses of the Fuller map, let me credit seven plusses:
1) Its unbroken continents;
2) Its relative lack of continental distortion (except Korea and vicinity, and Norway);
3) Its whole-earth philosophy;
4) Its closed-system contiguity of all edges;
5) Its disregard of national borders (but also a drawback);
6) Its use for the World Game (but now moribund);
7) Its paternity of the geodesic dome.
But here is my assessment of its seven deadly design shortcomings, none of which afflict the Cahill map:
1) Asymmetry of layout;

2) Irregularity of graticule; e.g.:

a)  22 separate graticule patterns; each facet is different;

b)  Equator bent, curved, and scattered,

c)  Most other meridians and parallels also bent, warped, or scattered;

d)  Poles are irregular ovoids;

e)  Adjacent geocells often misshapen, disparate, or broken;

f)  Poor matchup of graticule from one facet to the next

g)  No meridian or parallel on an icosahedral Dymaxion map is true to scale: only the triangle edges are, none of which track lines of latitude or longitude.

and because of all that

h)  Graticule is diminished, downplayed, or omitted. and:

i)  The other major flaws are exacerbated, namely:

3) Bad distortion of Korea and vicinity; also Norway; demonstrating:

4) Poor scalability: the larger a Dymaxion map, the worse it looks, if it has 5º or 1º geocells; otherwise its artistic license conceals the dirty laundry of its messy graticule. A Cahill map-and-graticule is good at any scale from smallest to largest.

5) Anti-metric measurements; triangle edges have unstated irrational metric length of 7,048.89 km (unlike Cahill-Keyes facet edges of 10,000 km);

6) Poor to zero comparison with any equivalent globe (none exist anyway, short of my improvisational photos in Part 9.7); therefore,

7) Poor synoptic globe-and-map learnability: unlike a paired octahedral globe-and-map (Cahill).
Add to that the frequent misstatements by Fuller et al that the Dymaxion Map was the first to show the continents undistorted and unbroken; was the first to get a patent; etc., when Cahill had already done all three, over thirty years earlier. (And without distorting East Asia and Norway, as does Fuller.)

Part 9.1
Asymmetry of layout

We begin with symmetry: Cahill has it; Fuller does not.

Compare these two maps: Fig. 9.1.1 is a Cahill version from 1920. Fig. 9.1.2 is Fuller's 1954 icosahedral, as printed in 1962 I chose these because both have comparable black continental silhouettes, and continental layouts, and adjusted their scales so that each is at 1/200,000,000.
Source notes:

Fig. 9.1.1:
B.J.S. Cahill, "A Unique Commercial Atlas and World Map" (Pacific Marine Review, [1920]-03) p. 112. Scanned and digitally remastered with ClarisWorks by Gene Keyes from an illustration in a different layout in B.J.S. Cahill, "The World Through German Goggles" (Pacific Marine Review, [ca. 1919-11]. Map enlarged to 208% of original. (Offprint quality of latter better than Xerox of former.)

Fig. 9.1.2:
R. Buckminster Fuller, Education Automation (Carbondale and Edwardsville: Southern Illinois University Press, 1962) p. 2. Map reduced to 71% of original.
Fig. 9.1.1: Cahill octahedral, 1909
Symmetry of B.J.S. Cahill octahedral Butterfly World Map, Pacific layout
Fig. 9.1.2:
Fuller icosahedral, 1954
Dymaxion map, 1954 icosahedral, asymmetrical layout, compared to B.J.S. Cahill's octahedral

Remarks: The Fuller design is grossly asymmetrical, especially compared to Cahill's total symmetry. (And that is without regard to Fuller's completely irregular graticule, discussed in Part 9.2. Not only is the exterior framework asymmetrical, but so is the interior grid of every single triangle.) As well, we have those four sore-thumb pieces at Antarctica and Oceania, from two  triangles, each with a different split, resulting in 22 pieces rather than 20. Even without such a split (which I don't think was needed; see Part 6, Fig. 6.5), the Dymaxion icosahedron lacks a symmetrical layout, such as a sub-logo of the Buckminster Fuller Institute:

Fig. 9.1.3
BFI sub-logo
Source: http://challenge.bfi.org/ideaindex

Fig. 9.1.4: Nor, of course, does the Dymaxion icosahedral accord with the symmetrical diagram which accompanied its original 1954 publication:

Dymaxion map diagram
Source: (See Part 5.) Scanned by Gene Keyes from
R. Buckminster Fuller,
"Dymaxion Airocean World Fuller Projective Transformation"
[Raleigh, North Carolina, 1954; l large folded sheet, 13x19", 33x49 cm, to accompany the Raleigh Edition of the Dymaxion Map.]
(Diagram also seen at p. 702, Fuller, Synergetics, [vol. 1])

Barring the octahedral's incisions, Cahill has 10 main outer edges. Fuller has 26. I will elaborate in Part 9.7 about how the complex asymmetry of the Dymaxion icosahedral makes it far more difficult to "learn a globe" than a pairing of Cahill and a globe. Suffice to say here that a simple glance at the outline of the Fuller and the Cahill adjacently makes it evident that Cahill has the elegant design.

Next, consider the continental profiles of those two maps. They are essentially similar (though regarding Fuller's "imperceptible" distortion, one might see his South America and Australia are a bit shrunken). Fuller avers that his map shows continuity across the Arctic area; I argue (in more detail below) that the result is an unacceptable distortion of Korea and vicinity. Meanwhile, notice in the two maps above, how the act of "pulling" Eurasia closer to Greenland in the Dymaxion causes its rupture of East Asia, tearing Korea 60º from the mainland.

Admittedly, this 1920 version of Cahill does not show Antarctica, but that is easily remedied by attaching the icy continent to the apex of any of the octants, as I have done in the Cahill-Keyes revision (see top of this page, and also here). Reuniting Antarctica is also more possible with Cahill's 1936 "C" model shown in Part 9.2 next, because it has right-angle vertices, instead of curved.

Furthermore, various alternate tile arrangements in a Cahill map, e,g, Butterfly profiles joined at Atlantic or Pacific, and ditto for "M" profiles; etc., not only retain octahedral symmetry, but unbroken continents as well. A Cahill map thereby has more flexibility and versatility than Fuller's. Alternate tile arrangements in a Fuller map not only aggravate its asymmetry, but break the continents.

Not that I am obsessed about symmetry, though I certainly prefer it. (I will say that Cahill himself went too far with symmetry when he decided to incise his map by 22 1/2º, and to divide the globe at 22 1/2º W, instead of the far preferable 20º W.)

However, my essential argument, further on, is how the simple symmetry of the Cahill design facilitates balanced comprehension of the globe. Fuller's raggedy layout does not. His icosahedron further disorients the user because of its non-alignment to the global axis, its non-alignment to any parallel or meridian, and hence its non-alignment to a globe.

Which brings us to the second fatal flaw of the Dymaxion map: its deplorable graticule.

Go to Part 9.2
Total Irregularity of Graticule

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