Nexorades/Rotegrities - Frequencies 1 through 3

1,848 views
Skip to first unread message

TaffGoch

unread,
Jul 28, 2016, 10:50:49 PM7/28/16
to Geodesic Help Group
Here is the extent of what I've modeled, in order of increasing parts "density":
Inline image 1
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

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

Inline image 1

Inline image 2

Inline image 3

Inline image 4

Inline image 5

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.

Inline image 6

-Taff

TaffGoch

unread,
Aug 3, 2016, 1:00:13 AM8/3/16
to Geodesic Help Group
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:
Inline image 1
(Essentially, all pentagons are, now, the same size.)

Radius ratio, smallest:largest = 1:3.44

-Taff

biagiodicarlo

unread,
Aug 3, 2016, 4:21:18 AM8/3/16
to geodes...@googlegroups.com
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:
<Nexorades; pentagon scale.png>
(Essentially, all pentagons are, now, the same size.)

Radius ratio, smallest:largest = 1:3.44

-Taff

--
--
You received this message because you are subscribed to the "Geodesic Help" Google Group
--
To unsubscribe from this group, send email to GeodesicHelp...@googlegroups.com
--
To post to this group, send email to geodes...@googlegroups.com
--
For more options, visit http://groups.google.com/group/geodesichelp?hl=en

---
You received this message because you are subscribed to the Google Groups "Geodesic Help Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email to geodesichelp...@googlegroups.com.
For more options, visit https://groups.google.com/d/optout.

TaffGoch

unread,
Aug 16, 2016, 5:39:51 PM8/16/16
to Geodesic Help Group
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


Inline image 1

Inline image 2

-Taff

TaffGoch

unread,
Aug 16, 2016, 7:43:53 PM8/16/16
to Geodesic Help Group
Some physical examples -- then and now....

Richard Boyt's rotegrity:
Inline image 1

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

Father Magnus Wenninger's "Order in Chaos" has a rotegrity quality to it:
Inline image 3

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:

Inline image 4

Inline image 7

Inline image 6

Inline image 8

Inline image 10

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

-Taff

TaffGoch

unread,
Aug 16, 2016, 11:20:44 PM8/16/16
to Geodesic Help Group
Spotted online: Kortrijk, Belgium -- May 2016 street festival
Inline image 1

-Taff

TaffGoch

unread,
Aug 17, 2016, 12:03:12 AM8/17/16
to Geodesic Help Group
​Hiroshi Murata's "Da Vinci Dome" has a 3v{0,3} spherical rotegrity basis​:
Inline image 1

-Taff

TaffGoch

unread,
Aug 23, 2016, 7:03:41 PM8/23/16
to Geodesic Help Group
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

Inline image 2
___________________________________

I've also modeled the Terraform "Plug-In Ecology," in two versions:
Inline image 1

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

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

-Taff
Message has been deleted

TaffGoch

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

-Taff

Rikus Keyser

unread,
Jan 31, 2018, 3:16:13 PM1/31/18
to Geodesic Help Group
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

unread,
Jan 31, 2018, 9:26:35 PM1/31/18
to Geodesic Help Group
Rikus,

Your formula interpretation (calculation) is correct.

-Taff

Rikus Keyser

unread,
Feb 1, 2018, 1:56:40 AM2/1/18
to Geodesic Help Group
Thank you very much!

R.

Rikus Keyser

unread,
Feb 17, 2018, 1:23:45 AM2/17/18
to geodes...@googlegroups.com, taff...@gmail.com
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

--
--
You received this message because you are subscribed to the "Geodesic Help" Google Group
--
To unsubscribe from this group, send email to GeodesicHelp+unsubscribe@googlegroups.com

--
To post to this group, send email to geodes...@googlegroups.com
--
For more options, visit http://groups.google.com/group/geodesichelp?hl=en

---
You received this message because you are subscribed to the Google Groups "Geodesic Help Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email to geodesichelp+unsubscribe@googlegroups.com.
Rotegrity scale model.jpeg

Ashok Mathur

unread,
Feb 17, 2018, 8:30:44 PM2/17/18
to geodes...@googlegroups.com, TaffGoch
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

unread,
Feb 18, 2018, 4:44:28 AM2/18/18
to Geodesic Help Group
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


To unsubscribe from this group, send email to GeodesicHelp...@googlegroups.com

--
To post to this group, send email to geodes...@googlegroups.com
--
For more options, visit http://groups.google.com/group/geodesichelp?hl=en

---
You received this message because you are subscribed to the Google Groups "Geodesic Help Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email to geodesichelp...@googlegroups.com.

For more options, visit https://groups.google.com/d/optout.

--
--
You received this message because you are subscribed to the "Geodesic Help" Google Group
--
To unsubscribe from this group, send email to GeodesicHelp...@googlegroups.com

--
To post to this group, send email to geodes...@googlegroups.com
--
For more options, visit http://groups.google.com/group/geodesichelp?hl=en

---
You received this message because you are subscribed to the Google Groups "Geodesic Help Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email to geodesichelp...@googlegroups.com.
AB2018_WeR1_Theme Camp Sketch Proposal crop.jpeg

Ashok Mathur

unread,
Feb 18, 2018, 8:23:34 AM2/18/18
to geodes...@googlegroups.com
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


To unsubscribe from this group, send email to GeodesicHelp+unsubscribe@googlegroups.com

--
To post to this group, send email to geodes...@googlegroups.com
--
For more options, visit http://groups.google.com/group/geodesichelp?hl=en

---
You received this message because you are subscribed to the Google Groups "Geodesic Help Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email to geodesichelp+unsubscribe@googlegroups.com.

Ashok Mathur

unread,
Feb 18, 2018, 8:50:11 AM2/18/18
to geodes...@googlegroups.com
 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

unread,
Feb 18, 2018, 2:09:54 PM2/18/18
to Geodesic Help Group
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

unread,
Feb 23, 2018, 6:36:33 PM2/23/18
to geodes...@googlegroups.com
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


To unsubscribe from this group, send email to GeodesicHelp+unsubscribe@googlegroups.com

--
To post to this group, send email to geodes...@googlegroups.com
--
For more options, visit http://groups.google.com/group/geodesichelp?hl=en

---
You received this message because you are subscribed to the Google Groups "Geodesic Help Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email to geodesichelp+unsubscribe@googlegroups.com.

For more options, visit https://groups.google.com/d/optout.



--

------------------------------------------------------------------------------------

D.A.L.E.!

~   "Despertando a la Ecosofía"   ~

-----------------------------------------------------------------------------------

TaffGoch

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

I safely downloaded from AzaFran's link, with no kerfuffle.

-Taff

Yves Rolland

unread,
Jul 24, 2018, 11:20:04 AM7/24/18
to Geodesic Help Group
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

unread,
Dec 26, 2018, 5:18:18 AM12/26/18
to Geodesic Help Group


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

unread,
Jan 18, 2019, 1:57:07 AM1/18/19
to Geodesic Help Group
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

unread,
Feb 7, 2019, 1:24:58 PM2/7/19
to geodes...@googlegroups.com
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.

--

Ashok Mathur

unread,
Jan 19, 2020, 10:41:41 AM1/19/20
to geodes...@googlegroups.com
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




--

Bill F

unread,
May 16, 2020, 3:04:55 AM5/16/20
to Geodesic Help Group
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 .

unread,
May 16, 2020, 3:32:21 AM5/16/20
to geodes...@googlegroups.com
Bravo! Great work Bill, and cheers to TaffGogh!

--
--
You received this message because you are subscribed to the "Geodesic Help" Google Group
--
To unsubscribe from this group, send email to GeodesicHelp...@googlegroups.com
--
To post to this group, send email to geodes...@googlegroups.com
--
For more options, visit http://groups.google.com/group/geodesichelp?hl=en

---
You received this message because you are subscribed to the Google Groups "Geodesic Help Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email to geodesichelp...@googlegroups.com.

Levente Likhanecz

unread,
May 16, 2020, 8:19:43 AM5/16/20
to Geodesic Help Group

Levente Likhanecz

unread,
May 16, 2020, 9:06:45 AM5/16/20
to Geodesic Help Group
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:
--

TaffGoch

unread,
May 16, 2020, 9:56:51 PM5/16/20
to Geodesic Help Group
Hi, Bill,

Commendations on your work's style and beauty

-Taff
(aka, David Price)

Edward Popko

unread,
Aug 31, 2020, 11:10:22 AM8/31/20
to Geodesic Help Group
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

Adam Winter

unread,
Aug 31, 2020, 1:34:35 PM8/31/20
to geodes...@googlegroups.com
What's the first edition called?

--
--
You received this message because you are subscribed to the "Geodesic Help" Google Group
--
To unsubscribe from this group, send email to GeodesicHelp...@googlegroups.com
--
To post to this group, send email to geodes...@googlegroups.com
--
For more options, visit http://groups.google.com/group/geodesichelp?hl=en

---
You received this message because you are subscribed to the Google Groups "Geodesic Help Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email to geodesichelp...@googlegroups.com.
Reply all
Reply to author
Forward
0 new messages