Basket Weave

[Biagio Di Carlo]

Dear Taff,
please can you draw the 4v alt icosa basket weave sphere ?

I made a paper model based on the Bamboo Dome in DB2 pag 95:
(s) short= 0.2603 (m) medium= 0.3103 (l) long=
0.3263
But the model it is not very spherical.

By giving a look on page 109 of DB2 (4v Icosa alt) I found that:
s=B= 0.2952 m=C= 0.2945 l= E= 0.3249

Maybe there is an error in the chord factors?

Probably the best way to dissipate doubts is to draw the sphere with SUp
founding the new CFs.

bdc

[TaffGoch]

Biagio,

You caught me (1400 km) out-of-town, visiting family for the holidays.

I have not yet calculated or measured the chord factors or angles, but I can tell you that the Domebook2 bamboo dome is geometrically-based on the attached figure. This was modeled in SketchUp, without measurements, except for rotation angles.

There is only one correct geometry, since the bamboo arcs are PLANAR, and are defined by the depicted LESSER-CIRCLES.

As soon as time permits, I will measure the chords, as well as arc lengths between intersection nodes. It should come out the same as that in Domebook2, if those numbers are indeed correct.

-Taff

[Biagio Di Carlo]

Dear Taff,

thank you very much for the very useful drawing.

If you have time, more data are welcomed.

BDC

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[Gerry in Quebec]

Hi Biagio (& Taff),
The three numbers listed for the bamboo dome described in Domebook 2
(p. 95), and ascribed to Buckminster Fuller, are "arc factors", not
chord factors. They translate into the following chord factors:
BB: 0.25957
BR: 0.30907
RR: 0.32492

These match the chord factors (to four decimal places) that David
Kruschke, in his 1972 booklet Dome Cookbook of Geodesic Geometry (p.
29), ascribes to Fuller's truncatable 4v icosa:

0.2596
0.3091
0.3249

The first two numbers differ from their counterparts in method 1 of
the 4v icosa (class I), which are 0.29524 and 0.29453.

Even though the bamboo dome is not fully triangulated and is based on
a set of lesser circles (12?), not great circles, the Fuller quotation
in Domebook 2 refers to this structure as a "geodesic dome". (You may
recall the earlier posts by Katrina Howard Fairley about the
difference between geodesic and non-geodesic domes.)

Historical tidbit: According to Kruschke, Fuller knew the chord
factors of the truncatable versions of at least the 3v and 4v icosa
(class I) years before the Domebooks were published. Yet the Domebook
authors didn't believe Kruschke when he told them it was possible to
have a 3v icosa dome in which all the vertices at ground level lie in
the same plane. Seems ironic that the flat truncation option, at least
for the 4v icosa, was right under their noses -- in the description of
the bamboo dome. Except for the smaller number of vertices and struts,
that basic design is still used by builders, including Blair Wolfram
at Dome Inc., Dennis Johnson at Natural Spaces, Wil Fidroeff who makes
the EconOdome, and Timberline Geodesics, all in the USA, and Robbie
Lusher at The Dome Company, in Sydney, Australia.

Cheers,
- Gerry

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[Gerry in Quebec]

Biagio,
A couple of further points about that basket weave dome.... The design
shown in Domebook 2 makes it look as if the bamboo struts are arcs,
following the curvature of the circle. But I suspect that if you try
to build a model with sections of bamboo or some other stick material,
you'll end up with struts that are closer to chords than arcs. So, it
might be better to use the chord factors, not the arc factors, for a
bamboo-stick model.

As for your paper model, I assume it's a set of "panels" taped
together -- regular pentagons, two types of triangles, and
"hexagons".... Right? If so, you'll probably end up with distortions
(non-sphericity) no matter which numbers you use. This is because the
six vertices defining each hexagon are not co-planar.

Cheers,
- Gerry in snowy Quebec

[Biagio Di Carlo]

Dear Gerry,

thank you for the answer.

This is the irregular  model that I have done with 

(s)  short= 0.2603          (m) medium= 0.3103            (l) long=0.3263

It is made with 12 lesser circles.

You suggests to use the Kruschke  chord factors.  

0.2596

0.3091
0.3249

On page 109 of DB I found:

B= 0.2952

C= 0.2945

E= 0.3249

What is the correct solution ?

bdc

[Gerry in Quebec]

Hi Biagio,
Don't use the chord factors on p. 109 of DB. That geometry differs
from the geometry of the bamboo dome on p. 95 and from Taff's SketchUp
model.

If you want to build a full-size dome with bamboo (or other slightly
flexible tubing), as described on p. 95, then follow Fuller's
instructions and use his ARC factors (0.2603, 0.3203, and 0.3263) to
construct the two types of composite struts.

But if you want to build a very SMALL model (i.e., using short, stiff
pieces of bamboo or other material, which might not bend enough to
follow the required spherical shape), it might be wise to use Kruschke/
Fuller's CHORD factors (0.2596, 0.3091 and 0.3249). These two sets of
numbers (arcs vs CFs) are pretty close in value. My gut feeling is
that, in the "real world", the lengths needed to produce a SMALL,
close-to-spherical bamboo basket-weave dome will be somewhere between
the arc factors and the chord factors......

But I guess that's splitting hairs. :-)

- Gerry

On Dec 23, 1:18 pm, Biagio Di Carlo <biagiodica...@gmail.com> wrote:
> Dear Gerry,
> thank you for the answer.
> This is the irregular  model that I have done with
> (s)  short= 0.2603          (m) medium= 0.3103            (l)
> long=0.3263
> It is made with 12 lesser circles.
>
> You suggests to use the Kruschke  chord factors.
> 0.2596
> 0.3091
> 0.3249
>
> On page 109 of DB I found:
> B= 0.2952
> C= 0.2945
> E= 0.3249
>
> What is the correct solution ?
> bdc
>

[Gerry in Quebec]

Oops.... I meant arc value 0.3103 as you stated, not 0.3203.
- Gerry

[Dondalah Proust]

Hi Gerry, I don't think Bucky was giving a complete definition of a geodesic dome with this example.  You have to be able to tessellate a true geodesic dome.  In the case of the "basket weave" dome, how do you tessellate lesser circles to any desired frequency?

Happy New Year to all, Dondalah

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From: Gerry in Quebec <toomey...@gmail.com>
To: Geodesic Help Group <geodes...@googlegroups.com>
Sent: Friday, December 23, 2011 6:03 AM
Subject: Re: Basket Weave

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[Biagio Di Carlo]

For this model I have used the CFs by Kruschke:
short= 3997    medium= 4760     long= 5003
(I multiplied all the 3 original values for 154)

It is a good dome but not very spherical. 
Maybe this kind of  dome  will  never be very spherical.....

BDC

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