# Nexorades/Rotegrities - Frequencies 1 through 3

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### TaffGoch

Jul 28, 2016, 10:50:49 PM7/28/16
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Here is the extent of what I've modeled, in order of increasing parts "density":

1v {0,1} (icosahedron) (original "Rotegrity" by Richard Boyt, 1970)
2v {1,1} (i.e., class-II)
2v {0,2} (i.e., class-I)
3v {2,1} (i.e., class-III)
3v {0,3} (i.e., class-I)

I don't expect to fine-tune any higher frequencies, to achieve equal 1/3rd band subdivision (as it's a real pain to iteratively-produce manually, in SketchUp.) Also, the density of parts has reached a maximum practical count for actual construction of physical models.

Now, I just have to find an inexpensive, readily-available source of semi-flexible material to use for the bands (one to one-and-a-quarter inch width.) Any suggestions?

-Taff

### TaffGoch

Aug 1, 2016, 9:35:29 PM8/1/16
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By request, I have posted dimensioned images to my deviatART webpage gallery:

These dimensions will produce spheres of unit (1.000000) radius. As with geodesic chord factors, multiply by your objective radius, to make bands that will assemble desired-size spheres.

-Taff

### TaffGoch

Aug 3, 2016, 1:00:13 AM8/3/16
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If the band from the first rotegrity (icosahedron) is used as the pentagon bands of the other four "nexo-rotegrities," the scale of sphere complexity becomes more apparent:

(Essentially, all pentagons are, now, the same size.)

-Taff

### biagiodicarlo

Aug 3, 2016, 4:21:18 AM8/3/16
Thank you very much, Taff !!
A very interesting work.

- Biagio

Il giorno 03 ago 2016, alle ore 07:00, TaffGoch <taff...@gmail.com> ha scritto:

If the band from the first rotegrity (icosahedron) is used as the pentagon bands of the other four "nexo-rotegrities," the scale of sphere complexity becomes more apparent:
(Essentially, all pentagons are, now, the same size.)

-Taff

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### TaffGoch

Aug 16, 2016, 5:39:51 PM8/16/16
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Final rotegrity "catalog"

I can't imagine anyone having the fortitude to construct any of the frequency-4 rotegrities - they're composed of a LOT of bands

-Taff

### TaffGoch

Aug 16, 2016, 7:43:53 PM8/16/16
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Some physical examples -- then and now....

Richard Boyt's rotegrity:

2v{0,2} geometry -- Drawing from "Rotegrity" leaflet, Parity Products, simple science toys, Eugene, OR (apparently, now defunct)

Father Magnus Wenninger's "Order in Chaos" has a rotegrity quality to it:

Other than these, I can't find any examples, from past decades.
___________________________

Recently, rotegrities are being studied, as "nexorades." I found an art project that employs 2v{0,2} geometry -- that of the Terraform "Plug-In Ecology" project:

Have you come across any other online examples (other than the group) ???

-Taff

### TaffGoch

Aug 16, 2016, 11:20:44 PM8/16/16
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Spotted online: Kortrijk, Belgium -- May 2016 street festival

-Taff

### TaffGoch

Aug 17, 2016, 12:03:12 AM8/17/16
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​Hiroshi Murata's "Da Vinci Dome" has a 3v{0,3} spherical rotegrity basis​:

-Taff

### TaffGoch

Aug 23, 2016, 7:03:41 PM8/23/16
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For those who want the actual 3D geometry (rather than just pretty pictures,) I've posted the rotegrity "catalog" SketchUp model to the 3D Warehouse:  Rotegrities - Pentagon Scale

___________________________________

I've also modeled the Terraform "Plug-In Ecology," in two versions:

Without the large pentagon "entrance":  Terraform "Plug-In Ecology"

With the pentagon "entrance":  Terraform "Plug-In Ecology" - Pentagon

-Taff
Message has been deleted

### TaffGoch

Aug 24, 2016, 9:50:49 PM8/24/16
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Note:  My references to "Terraform" should have been "Terreform"

-Taff

### Rikus Keyser

Jan 31, 2018, 3:16:13 PM1/31/18
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Hi Taff

Your work is so fascinating. I am interested to build a 2v{1,1} rotegrity of 1 meter in diameter. (That is to say if I you kindly give me permission to do so.)
I just have a question regarding the formula as per your diagram attached. If radius is 0.5m, I take it the distance between the attachment points will be 0.5(0.252981) for the red bands. Or is it more complex than that to scale it up or down?

Many thanks for taking the time to answer me.
Kind regards
Rikus
WeR1 Soulstice 2018 Rotegrity Nexograde structure.png

### TaffGoch

Jan 31, 2018, 9:26:35 PM1/31/18
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Rikus,

Your formula interpretation (calculation) is correct.

-Taff

### Rikus Keyser

Feb 1, 2018, 1:56:40 AM2/1/18
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Thank you very much!

R.

### Rikus Keyser

Feb 17, 2018, 1:23:45 AM2/17/18
Hi

The 1m diameter scale model worked out perfectly!

Now for the real one. 3m diameter. :-) I'll send a picture of that one too in a few weeks (we only need it constructed end of April).

Thank you again so much. Without you this would not have been possible.

Warmest regards
Rikus

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Rotegrity scale model.jpeg

### Ashok Mathur

Feb 17, 2018, 8:30:44 PM2/17/18
Dear Rikus,

Congratulations on the successful building of 1m dome.
Fuller had found that materials do not scale up linearly, that is to say, if a material of one and quarter inch width worked perfectly for a length of 1 meter, then it might become soft/putty like when its length reaches say 2 meters.

Hugh Kenners refers to this as slenderness ratio.

You might consider making a part model of the hexagon and its 6 adjustsant triangles with the material of new lengths of same width as the 1 m dome.
By the way, can you describe in some detail what the bands are composed of and how did you drill holes in them?
Regards
Ashok

Regards

Ashok

### Rikus Keyser

Feb 18, 2018, 4:44:28 AM2/18/18
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Hi Ashok

Thank you very much for the response and advice.

The 1 m scale model was made of 3mm plain plywood. Lasercut. The holes were also drilled by laser. The plywood sections (50mm wide) are kept together with 3mm bolt, washer and nut.

For the full scale 3 meter structure we intend to use 9mm thick marine grade plywood (150mm) wide with 8mm bolts, nuts and washers. A central steelpole (20mm diameter) and steel base plates over the two podal hexagons will add structural integrity. Radial rods can also be added if necessary. This whole structure will then be bolted on a 5m high pyramidal base structure. [See attached conceptual image to see where we are going with this :-)]

Any suggestions will be most welcome. (We'll also run it by a structural enigineer before we proceed to the full scale structure.)
Kind regards
Rikus

Regards

Ashok

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AB2018_WeR1_Theme Camp Sketch Proposal crop.jpeg

### Ashok Mathur

Feb 18, 2018, 8:23:34 AM2/18/18
Dear Rikus,
Thanks for the details.
They show that you are going about in a good manner.
As far as your going to a structural engineer is concerned, before you give him any money, ask him if he has heard of Rene Motro of France?
Regards
Ashok

Regards

Ashok

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### Ashok Mathur

Feb 18, 2018, 8:50:11 AM2/18/18
Dear Rikus,
My point of view is that the standard structural engineering software (FEA/FEMA) is absolutely incapable of handling tensegrity structures.
There is a long thread in the group where I have explained my point of view.
Than I have been silent on the subject trying to research as to who has done anything to make the proper software for analyzing tensgrities.

The answer to that question is Rene Motro of France.
The tensegrity wiki page has a good write up on him http://tensegritywiki.com/Motro%2C+Ren%C3%A9

Unfortunately, his English work, which costs more than \$ 1,000, is completely out of print.
https://www.amazon.com/Tensegrity-Structural-Systems-Ren%C3%A9-Motro/dp/1903996376

I was in USA last summer at Mountain View and I initiated a California wide search for a copy of his book in any public library.
It simply was not present.

To my knowledge, his software was last updated in year 2,000. There might be later editions, but I am not aware of them.
From the internet, you can download this MSc thesis of a student of his

Tensegrity Structures  and their Application to Architecture
Valentín Gómez Jáuregui

If there are French speaking readers who know more of his work, I would welcome their contributions.
Regards
Ashok

Regards

Ashok

### Rikus Keyser

Feb 18, 2018, 2:09:54 PM2/18/18
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Dear Ashok

Thank you so much for all the information. I'll look into the links you have shared. I'll speak to the engineer, but I am sure he would not have heard of René Motro...

I'll keep you posted!

Kind regards
Rikus

### AzaFran

Feb 23, 2018, 6:36:33 PM2/23/18
Hi folks! thanks for share knowledge, expreriences, proyects and resources. i find a research/study copy online of tensegrity systems for the future you can download at: http://b-ok.org/dl/871005/c716ea

Kind Regards

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### TaffGoch

Feb 23, 2018, 7:09:13 PM2/23/18
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An important book, hard to find a safe internet link for it.

-Taff

### Yves Rolland

Jul 24, 2018, 11:20:04 AM7/24/18
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Dear TaffGosh,

I have read your communications about nexorades in the same time I was interested in Bamboo last year, and I have proposed a greenhouse "active Bamboubulle" in a FAB14 event that happened in Toulouse last week. Thank you very much (and to Olivier Baverel to). This spherical shape seems optimal because of its sphericity and there is no natural material like bamboo.
I send you a notice and here are a few pictures https://photos.app.goo.gl/RWvYGkLMg0RapKQ22 .
A big thank you again.

Yves Rolland

BambouBulle_Fabrication DIY français-anglais.pdf

### Olga

Dec 26, 2018, 5:18:18 AM12/26/18
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Hi Taff,

Do you perhaps have a calculation for rotegrity dome as excel? I found one that is unfortunately only available as a pdf.

kind regrds
Olga
calculation.docx

### ZelDome

Jan 18, 2019, 1:57:07 AM1/18/19
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Dear Mrs Olga,
Your pdf reminded me of a picture I saw earlier on mr. Hiroshi Murata Da Vinci dome page. I made the Excel table, found that it was the same dome (12x magnification). Soma facts are still unknown for me: What are a,b? Two legs (Hex) are similar, whitch is left of blue leg, which is right?
Warning: This is not a dome calculation. No geometric analysis was carried out nor the dome was physically fabricated. My table is just my impression of two pictures of the web with the aim to help you. For the correct information and procedure, please order Mr. Murata manual.
Best regards,

ZelDome

Rus_Jap_dome.xlsx

### Olga M

Feb 7, 2019, 1:24:58 PM2/7/19
Thank you ZelDome.
a and b are distances between legs on the floor. I have build a small dome of 50 cm diameter  - it works.

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### Ashok Mathur

Jan 19, 2020, 10:41:41 AM1/19/20
Dear Taff
I have not thanked you for pointing out the link to Rene's book.
I am looking at it keeping in view Hector's requirements.
Thanks

Ashok

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### Bill F

May 16, 2020, 3:04:55 AM5/16/20
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Hello TaffGogh,

I built a rotegrity art piece based on your work and wanted to share the results with you.
It is built out of aluminum and I made some modifications.
I flipped it inside out because I liked the weave-like look. I also added another internal layer and a central pillar for strength. The two layers sandwiches CNC cut and engraved acrylic panels.

Thank you for your inspiration and posts on how to make one.

Bill Frymire

### lemondealc .

May 16, 2020, 3:32:21 AM5/16/20
Bravo! Great work Bill, and cheers to TaffGogh!

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### Levente Likhanecz

May 16, 2020, 8:19:43 AM5/16/20
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### Levente Likhanecz

May 16, 2020, 9:06:45 AM5/16/20
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hi Bill here is some compiled rotegrities in excel (macros are for sheet navigation)

On Sat, May 16, 2020 at 9:04 AM Bill F <bill.f...@gmail.com> wrote:
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### TaffGoch

May 16, 2020, 9:56:51 PM5/16/20
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Hi, Bill,

Commendations on your work's style and beauty

-Taff
(aka, David Price)

### Edward Popko

Aug 31, 2020, 11:10:22 AM8/31/20
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TaffGoch
We are preparing the second edition of a college textbook on geodesics and spherical subdivision and would like to include a vignette about your work.
Can you contact me?
ESP2

Aug 31, 2020, 1:34:35 PM8/31/20
What's the first edition called?

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