Origin of "method 1" triangle subdivision, class I?

[Gerry in Quebec]

Does anyone know the origin of "method 1" triangle subdivision for icosahedral and octahedral domes? In Geodesic Math and How to Use It, Hugh Kenner explains method 1 but only mentions briefly in a footnote (pp. 64) that the terminology comes from Joe Clinton and Domebook 2, without further references. Domebook 2 (p. 106) says: "This method is what was published in Domebook One under the name "alternate"; and is the geometry of the Pacific Dome, Aluminum Sun Dome, Pillow Dome, etc."

Method 1 is still probably the most widely used triangle subdivision method among do-it-yourself builders of small domes. It is also the method used for calculating strut lengths on DesertDomes and other websites. Example: chord factors for a 3v icosa, class I, method 1 dome are 0.3486, 0.4035 and 0.4124.

What I'm hoping to find out is who devised method 1, when, and whether there are any supporting documents available.

Thanks,

- Gerry Toomey

[TaffGoch]

Gerry,

From "Domebook 1"

The referenced NASA contract document is attached. The "triacon" method (class-II) is NOT covered. The "alternate" to the triacon method is what is now called "class-I". This report is one (November 1968) of a couple of "progress reports," so I'm guessing that this is the right one. (The other progress report covers the use of the "jitter-bug" concept for spacecraft.)

In the forward to the progress report:

"Personnel participating in the research include

Julian H.. Lauchner, principal investigator,

R. Buckminster Fuller,

Joseph D. Clinton,

Mark B. Mabee,

Richard M. Moeller, and

Richard Flood."

_______________________________

The final report was published in two parts, in September 1971. The concepts covered in the progress reports are incorporated therein. (Of note: Seven subdivision methods are described):

NASA CONTRACTOR REPORT; NASA CR-1735

ADVANCED STRUCTURAL GEOMETRY STUDIES

Part I - Polyhedral Subdivision Concepts for Structural Applications

Part II - A Geometric Transformation Concept for Expanding Rigid Structures

Joseph D. Clinton

Southern Illinois University

Carbondale, Illinois

-Taff

[TaffGoch]

​​

Note

​​

: 

​

Julian H. Lauchner was the dean

​ of the College of Engineering, at SIU​

​, in 1968

​

[TaffGoch]

Participants, listed in the final report (1971):

 - Lauchner, principal investigator

 - Clinton, prime investigator

 - Fuller, research consultant

Computer programmers:

 - Booth, Garrison, Keeling, Kilty, Mabee & Moeller

_____________________

I also recognized some relevant names in the bibliography:

 - H.S.M. Coxeter, 

 - Edward Popko, and 

 - Stuart Duncan

[TaffGoch]

Attachment:

[TaffGoch]

Attachment:

NASA CONTRACTOR REPORT; NASA CR-1735
ADVANCED STRUCTURAL GEOMETRY STUDIES

Part II - A Geometric Transformation Concept for Expanding Rigid Structures

​​

Note: CR-1734 is

​"​

Part I,

​"​

an

​d​

CR-1735 is

​"​

Part II

​"​

(I mistakenly referenced Part I, earlier, as CR-1735)

[Gerry in Quebec]

Thanks, Taff. I've downloaded the reports (I had already read one of them.) While these date back to the late sixties and early seventies, method 1 was around for some years before that, and as you know, it was used for Alvin Miller's "Pease" panel dome built for Bucky and Anne in April 1960. Duncan Stuart is credited with coming up with the method 3 subdivision for class II, some time around 1950. I'm wondering whether he or maybe Miller had a hand in developing the class I (alernate) methods, particularly method 1.

- Gerry

[Gerry in Quebec]

Here's a quote, the result of a Google search, about Don Richter's role in advancing dome geometry. Unfortunately that particular part of the book isn't currently available on Google Books.

"During this same time period [circa 1951] one of Fuller’s students, Don Richter, developed the 'Alternate' grid, figure 18, and Bill Wainwright of the Cambridge office Geometrics, Inc. developed the 'Alternate truncatable' grid, figure 16."

 

Reference: Parke, G.A.R., and P. Disney, eds. 2002. Space Structures 5, Volume 1, p. 428. London: Thomas Telford.

- Gerry in sunny Quebec