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Cahill 1909

Evolution of the Dymaxion Map:
An Illustrated Tour and Critique
Part 7

by Gene Keyes
2009-06-15

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 7
1995 ff: Dymaxion Maps on the Internet

Nowadays one can go to Google Images and fish out various Dymaxion maps of various types and sizes. Chris Rywalt in 1995 made a classic unfolding-animation of the icosahedron, and released it into the public domain. Here is his page of description and source codes: http://www.westnet.com/%7Ecrywalt/unfold.html, updated in 2003.

The animation is easily available at Wikipedia, so below I am showing some stills. While the animation itself is a fine piece of work; my objection is that it makes the icosahedral map look a lot simpler and more accurate than it really is in relation to a globe. I argue in Parts 8 and 9, that a Fuller map is much less comparable to a globe than a Cahill map.

Cahill very evenly and vividly divides the world with 3 strokes: Equator, and two meridians: eight pieces. He was able to demonstrate the principle with a rubber ball painted as a globe, and cut along enough of the incisions to squeeze it flat under a piece of glass; the ball would return to its globe shape once the glass was removed.

However, the icosahedron and its equivalent globe offer no such physical and visual transformation. Worse yet, Fuller's icosahedron does not comport with a globe's meridians and parallels — the graticule.

Rywalt's animation has done an excellent job as a virtual and graphical illustration of a Dymaxion map going from globe to icosahedron to flat map, but it is not a hands-on physical object. Furthermore, it does not show the graticule, and not even the triangles' dividing lines.

In reality, there is no pre-icosahedral earth-globe. And if there was one, it could not match the elegance and simplicity of either Cahill's ball, or a real globe with bold-ehancement of Cahill's 3 dividing lines.


We all can see that a geodesic dome — descendent of the Dymaxion map — is a thing of beauty. But it is also intricate, and ever more so as the frequency of the grid increases. I, for one, can admire a geodesic dome — like the famous one I visited in Montreal — but I cannot sort out its polygons by eye.

Likewise, a spherical icosahedron laid on a terrestrial globe is a complex and confusing affair, compared to an octahedral overlay. as well as compared to a global graticule. In a Cahill map, each octant preserves and replicates an identical graticule, as seen on a globe, and as seen laid out flat. The octants' poles are at one end; the Equator at the other. The parallels and meridians are in complete alignment with the boundaries of the octant.

Not so a Fuller icosahedral. The parallels and meridians clash in every way with the edges of every triangle. Fuller's great-circle gridwork is quite a different structure than a globe's lines of latitude and longitude. It is gorgeous on a geodesic bulding; it is something else again on a globe.

My point is, that the Dymaxion map animation looks great, but it is from a distance, and it omits the graticule. It is like beautiful pictures on a food package that do not live up to the contents.

If the same animation were done to a Cahill-type map, it could include the graticule, at any degree of closeness, and a smooth unrolling would be apparent, rather than the crazy-quilt degeneration suffered by the asymmetrical Dymaxion and its asymmetrical graticule, but not visible here.

Having said that, I still enjoy watching Rywalt's animation do its thing.