Re: How does Paul Robinson (Geo-dome) design his domes with one dihedral angle?

[Gerry in Quebec]

Johnny,

This August 2016 conversation, under the topic Help for a carpenter, may be of interest to you:

https://groups.google.com/d/topic/geodesichelp/nrT6xiXCyyw/discussion

- Gerry in Québec

On Wednesday, April 26, 2017 at 1:10:03 PM UTC-4, Johnny Bayles wrote:

I've built a couple of domes as per Paul's plans, and I plan to keep supporting his business because his designs and instruction have helped me go from a distant admirer or domes to actually building them!

However, I would like to experiment with my own designs as well. I am trying to model a 4v icosa for bevel frame construction but I am at a loss as to how Paul is able to model such beautiful domes using only one dihedral angle instead of 3 or 4??

Take this plan for example http://geo-dome.co.uk/domeshop/article.asp?Uname=273

Is this dome based off different geometry or frequency? I know he will sometimes use a lower frequency model for his panels and them build in another triangle to further divide the panel, thus 'faking' the frequency.... is that what's going on here?

Thanks in advance for any help, just trying to become a little more independent in the dome world. 

Cheers to people like Paul for being an inspiration!

[Gerry in Quebec]

Johnny,

The 3-frequency Geodome plan you mentioned appears to use so-called "method 1" geometry. Excluding the custom triangles to accommodate the door, this dome design has only two triangle types, but the 15-sided base does not sit perfectly flat. The uneven base is evident in Paul Robinson's diagram. An alternative geometry, sometimes called the Fuller-Kruschke method, or simply the Kruschke method, uses three types of triangles and has a level base in both the low- and high-profile versions of the dome (truncated either just above or just below the equator). There a discussion of it on the Geodome website here:

http://geo-dome.co.uk/forum/article.asp?uname=313

You can also find info on the 3v and 4v Fuller-Kruschke domes in this discussion group, using the Search function.

[Ashok Mathur]

Dear Johnny,

There is nothing special about using a single dihedral in icosa based domes upto 3v.

The difference between the required dihedral angle and the single averaged angle is slight enough to be overlooked.

For low radius domes, there is no need for making the bottom absolutely planner.

These do not hold in 4v domes.

I have not explored further higher domes.

Regards

Ashok

Regards

Ashok

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[Ashok Mathur]

Dear Johnny,

In our case, this was done some 30 years ago and I have no real information about how it was done.

Because it works, no one has gone back to study what was done.

But what you suggest - arithmetic mean- may be the right way to do.

Regards

Ashok

Regards

Ashok

On Fri, Apr 28, 2017 at 11:21 PM, Johnny Bayles <johnny...@gmail.com> wrote:

Thanks, Ashok.

Is there a way to average the 'required' dihedrals into one average one? Is it simply adding them and dividing by their number?

[Gerry in Quebec]

The attached image gives the results of adding up all the dihedral angles of two types of 4v icosa geodesic domes and then calculating the weighted averages of the bevel-rip angles for making struts for Oregon Dome-style triangular panels. Bottom line: 5 degrees.

- Gerry in Québec

On Saturday, April 29, 2017 at 12:57:14 AM UTC-4, Ashok Mathur wrote:

Dear Johnny,

In our case, this was done some 30 years ago and I have no real information about how it was done.

Because it works, no one has gone back to study what was done.

But what you suggest - arithmetic mean- may be the right way to do.

Regards

Ashok

Regards

Ashok

On Fri, Apr 28, 2017 at 11:21 PM, Johnny Bayles <johnny...@gmail.com> wrote:

Thanks, Ashok.

Is there a way to average the 'required' dihedrals into one average one? Is it simply adding them and dividing by their number?

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