A bit of history: Fuller, Kruschke & the 3v icosa dome
Gerry in Quebec
Tomorrow, August 31, marks exactly half a century since Buckminster Fuller was awarded patent no. 3,203,144 for the Laminar Geodesic Dome. One tidbit that caught my eye as I read the patent document some years ago was the list of chord factors used to determine the dimensions of the diamond-shaped panels of the 3v version of this type of dome. The numbers are the same as those calculated independently by David Kruschke in the late 1960s and published in his 1972 booklet, Dome Cookbook of Geodesic Geometry.
This is the same "flat base" geometry now used by various commercial dome builders including Blair Wolfram (Dome Inc./Hurricane Domes, Minnesota), Wil Fidroeff (EconoDome/FazeChange Produx, Illinois), Ernie Aiken (Garden Domes, Texas), Dennis O. Johnson (Natural Spaces Domes, Minnesota), Robbie Lusher (The Dome Company, Australia), and Timberline Geodesics (California). It's also the same geometry used in Popular Science's 1972 project plan no. 5544, The Bucky Fuller Hexa-Pent Dome, posted here by Paul Kranz the other day.
https://groups.google.com/forum/#!searchin/geodesichelp/Buckys$20dome.pdf
In early 2010, over on Paul Robinson's Geo-Dome website forum, someone asked about leveling the base of a dome. I had earlier made a small model of a 3v dome using David Kruschke's chord factors and a pile of plastic drinking straws. I took a webcam shot of it, traced it, labeled it, and posted the drawing and chord factors on Geo-Dome, referring to it as the "Fuller-Kruschke" version of the 3v icosa:
http://geo-dome.co.uk/forum/article.asp?uname=313
(Also re-posted here on Geodesic Help recently by Dick Fischbeck.)
Nearly three years later, David Kruschke posted the following clarification in the Geo-Dome thread:
".... I've seen Buckminster Fuller's chord factors for two and four frequency domes but I've never ever saw any 3 frequency chord factors he might have had. I independently derived the 3 frequency chord factors myself during the Fall of 1968 and later published my domebook that included these. I published the derivation because I didn't want people to use a geometry that they couldn't independently check before cutting materials. To this day, I've never seen the derivation of a three frequency dome geometry elsewhere that has a flat cut off plane at ground level..."
While the Fuller patent document that lists the 3v chord factors predates the Kruschke publication by about seven years, the latter is the only place I've seen the actual trigonometry. As far as I know, neither Bucky Fuller nor his colleagues ever published the math, just the chord factors. So David Kruschke's booklet remains a prized possession in my little collection of dome publications.
Paul Kranz
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