Kenner subdivision method, 6v example

[Gerry Toomey]

Here's a triangular subdivision method I don't think we've discussed before in this group. It's explained by Hugh Kenner in his book, Geodesic Math. The 6v dome in the illustration doesn't sit flat but it could be built with just 5 strut lengths.

- Gerry Toomey

[Paul Robinson]

That's an excellent design, I like that there are no scalene triangles, something that I've not seen on a 6v until this one.

.

Cheers,

Paul

On 22 Dec 2013, at 17:50, Gerry Toomey wrote:

Here's a triangular subdivision method I don't think we've discussed before in this group. It's explained by Hugh Kenner in his book, Geodesic Math. The 6v dome in the illustration doesn't sit flat but it could be built with just 5 strut lengths.

- Gerry Toomey

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<6v-icosa-classI-Kenner-Method.jpg>

[TaffGoch]

This may be comparable to what is produced by the so-called "parallel trihedra" method, which I found in a patent (if I recall, correctly.) There are, most-certainly, similarities. I'll have to investigate, further....

-Taff

[TaffGoch]

Ah, it wasn't a patent -- it was a journal paper:

___________________________

"Designing Optimal Spatial Meshes: Cutting by Parallel Trihedra Procedure"

J. L. Alvaro, C. Otero

Journal of the International Association for Shell and Spatial Structures: IASS

Vol.41 (2000) n.133

http://grupos.unican.es/egicad/docs/egi1030102enlace2.pdf

Good conceptual read....

-Taff

[TaffGoch]

Gerry,

I can confirm that Kenner's method and the method described in the Alvaro paper are, indeed, the same. My 3D modeling, using the Alvaro method, produced the following chord factors:

As you can see, the chord factors agree with your values. The Alvaro method that I used is best described by Figures 12 & 13, from his paper:

Since I used this "physical" construction method, rather than numeric calculation, this provides excellent confirmation of both, Kenner's method, and your calculations.

-Taff

[Gerry in Quebec]

Thanks, Taff. I did a quick scan of the Alvaro paper when you posted it and it looks really interesting.

- Gerry