strut calcs using the "Mexican" (GHT) method for up to 28v!

[David Zhang]

I updated my tool  with an improved function for equalizing chord factors using the GHT method for domes up to 28v.  I checked the calculations and they match the ones provided by Hector Hernandez in a previous post in this group (except for a slight  difference in 8v for one chord)

https://synesthes.is/geodesign

And If you just want the chord factors for 28v:

0.039538
0.040067
0.040574
0.041058
0.041521
0.041961
0.042379
0.042776
0.04315
0.043503
0.043834
0.044144
0.044432
0.0447
0.044946
0.045173
0.04538
0.045567
0.045735
0.045884
0.046015
0.046129
0.046225
0.046305
0.046369
0.046418
0.046451
0.046471

[Ashok Mathur]

Dear David

Can you post the chord factors for 8v and 9v domes.

Are the chord factors “nearly equal” or exactly equal either will do. I am just curious.

Regards

Ashok

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[David Zhang]

Ashok,

Here are my calculations for 8v and 9v.  i don't think you can get exact chord factors above 5v but these should be good enough for most purposes - a few of these chords are a few millimeters  (less than .0003) above or below the chord factor and i took the average.  i've included the exact calculations in parenthesis.

8v

0.138283
0.144406 (14.4405, 14.4406)
0.149584 (14.9582, 14.9583, 14.9584, 14.9585)
0.153824 (15.3822, 15.3823, 15.3824)
0.15715  (15.7149, 15.7151)
0.159608 (15.9606, 15.9609)
0.161257
0.162173

9v

0.122939
0.127821  (12.782, 12.7821)
0.132039 (13.2038, 13.2039)
0.135596  (13.5595, 13.5597)
0.138504 
0.140787 (14.0786, 14.0788)
0.142476 (14.2475, 14.2477)
0.143614
0.14425

[Bryan L]

That's pretty good David.

I have solved mathematically and got

0:1	0.138283173547168
1:9	0.162172586886607
1:10	0.144414185229293
2:10	0.161257357424252
2:11	0.149585989794198
3:11	0.15960800350164
3:12	0.153823205082127
4:12	0.157149991455025

The difference between chords 1:10 and 10:11 was 

1.16698888250055E-5

and between 2:11 and 11:19 was 

3.28790393300249E-6

I also solved with varying R to get exact chords and the difference in R for one or two vertices was about the same (miniscule for all intents and purposes)

Bryan

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[Ashok Mathur]

Thanks to both David and Bryan.

Now I need an assembly diagram like the one provided by Dome Calculator.

Thanks

I would like to say that Vigyan Ashram Pabal, with which institution I am associated as an occasional teacher, provided 3v domes in large numbers to people hit with an Earthquake. After 30 years or so they are still being used as homes. I can post some recent videos of such domes.

Thus domes do have good uses but still we need to enlarge the adoption of domes.

Regards

Ashok

To view this discussion visit https://groups.google.com/d/msgid/geodesichelp/CABWq%3Di6Wgp6yzOgn70U7CaEjOT%2BDkG7_MPSHVpWTsETVsp%3D9iw%40mail.gmail.com.

[Ashok Mathur]

This is a link to some photos and a video of domes built in Laur, a district of Mahrashtra, India after a devastating earthquake.

https://drive.google.com/drive/folders/1T5Bwhosh8iw-iTXr2f_X3JEXphW_1H38?usp=drive_link

Regards

Ashok

[Bryan L]

To view this discussion visit https://groups.google.com/d/msgid/geodesichelp/CAD-a3OgFC3BCz6ZrHwpypue58QONwG13D5k2DEyonciOo04O_Q%40mail.gmail.com.

[Ashok Mathur]

Thanks

Regards

Ashok

To view this discussion visit https://groups.google.com/d/msgid/geodesichelp/CABWq%3Di4pMN915rwthOGb_xA8H0BK1KZtK1V%2B3iAyhvZpazotZw%40mail.gmail.com.

[Bryan L]

Attached are my spreadsheets for solving Mexican V8 with either some struts not equal or some R not equal.

Hector gave me the outline of the method ages ago.

I wrote a post outlining it as best I could about the same time.

I tried to send these in a new thread but when sending from my email the post never appeared and when sending from Google Groups it would only allow images

as attachments...

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[David Zhang]

thank you Bryan!  I was wondering how the spreadsheet method worked.  

[David Zhang]

Here's a 16v tetrahedral.  Don't see a lot of these, but it would be a cool  to build one ^_^

 0.11934

0.13412

0.14827

0.16131

0.17277

0.17297

0.18276

0.18299

0.19126

0.19786

0.20282

0.20625

0.20741

0.20825

0.20845

0.20921

[Gerry in Quebec]

Hi David, Bryan, Ashok & others,

Just a reminder that when the Mexican subdivision is applied to the icosahedron, it doesn't give a flat base at any useful dome truncation, not even as a hemisphere. Image of an 8v geosphere attached.

David, what does GHT stand for?

- Gerry in Québec

[David Zhang]

Gerry,

I think it's people's initials. I got it from another post in this group a few years ago, where Hector Hernandez suggested a different name for the Mexican method. The H is Hernandez, and T is Taff.   Maybe you're the G?  ^_^

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[Hector Alfredo Hernández Hdez.]

I like it

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[Chris Kitrick]

Hi,

It must be noted that the 'Mexican' or GHT method is an approximation and if you don't relax the radius constraint then there are no exact solutions (except for a few cases).

The quality of solutions degrade from the icosahedron to the tetrahedron where each face comprises larger portions of the sphere surface. Thus the icosahedron has better quality than the tetrahedron. Quality is measured by how much difference is tolerated between edge lengths to call them equal. For the icosahedron the edge lengths I can resolve match the values posted by David Zhang.

Cheers,

Chris