Bamboo Model of My Version of a Reciprocal Frame Dome

[Robert Clark]

I'm finally building a 24" diameter physical model of my design using bamboo strips and 2-56 size screws.  It's a nexorade that consists of just one strut type repeated throughout. Despite having rectangular features, the structure is rigid do to the triangular components.  120 bamboo struts create a full sphere held together with 240 screws.

[Robert Clark]

Here is the finished sphere.  Not an object of any practicality, but perhaps enjoyable to look at.

[Gerry in Quebec]

Looks great, Robert. Are you planning to keep it outdoors as an art piece? And would the bamboo struts need some kind of protective coat?

- Gerry in Québec

[Adrian Rossiter]

Hi Robert

On Sat, 4 Nov 2023, Robert Clark wrote:
> Here is the finished sphere. Not an object of any practicality, but
> perhaps enjoyable to look at.

Very nice!

Adrian.
--
Adrian Rossiter
adr...@antiprism.com
http://antiprism.com/adrian

[Robert Clark]

Hi Gerry,

I do not plan to keep it outdoors.  I just took it outside for taking a picture because the lighting was better.

It might be possible to scale this up.  Eight foot long boards could could create a 24 foot diameter dome or sphere.  Could be used as a vine covered arbor if the wood was protected.

1/2" emt metal conduit pipes 10 feet long would create a dome frame of 30 feet in diameter.  with a large tarp over the top, it could be used as a storage area for a tractor or other things.

If anyone else has some ideas for such a frame, let me know.

Robert

[Dx G]

Those fiberglass straps they use to cover boats might be a good material. Lightweight, resilient, weatherproof.  Likely expensive though, and I'm unsure if its worth the cost.

 Also, wood lath is available in lots of places, although usually sold in 4 foot lengths.

There are a number of "domes" of sorts that are made from "hoops", typically from PVC pipe.  The plans are in several legacy dome books.  If there is interest in these, I can dig up some details.

https://www.youtube.com/watch?v=4n5WFkqq8WM   "star" dome

clamshell hoop dome

https://www.youtube.com/watch?v=yC5DEzsLK2M

 If you try one of these, you can strengthen the shell considerably if you tie a few lines between hoops (perpedicular to them), especially for snow load.

Then, of course, there are Dick's Randomes.

DxG

[Charles Lasater]

---------- Forwarded message ---------
From: Charles Lasater <charles...@gmail.com>
Date: Sun, Nov 5, 2023 at 2:52 PM
Subject: Re: Bamboo Model of My Version of a Reciprocal Frame Dome
To: <geodes...@googlegroups.com>

Hi Robert,

I have designed a similar sphere using 60 struts and constructed carports with 10' 3/4" rigid EMT. Here is the connection scheme.

Parachutes make great shade.

Best,

Charles

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[Robert Clark]

Charles,

Great connection idea.  I'd like to see a picture of your sphere.

I'm kind of forming an idea in my head for a way to connect the steel emt conduit in a cost effective and least labor intensive way.  What I'm picturing is:  wrapping the first 3 or 4 inches of the ends of the tubes in multiple layers of sticky cloth hockey tape, and also, wrapping the two connection points towards the middle. Then, I would begin lashing tubes to each other with a Square Lashing Knot using 18 gauge (.045") stainless steel lashing wire.  The wire, when twisted tight, should dig into the hockey tape and hold the tubes together without slipping.  A 30 foot diameter dome could be built for about $500 including (60) 1/2" x 10' emt conduit, hockey tape, stainless lashing wire, and plastic push-in caps for the tube ends.

Robert

[Charles Lasater]

Carport  22' dia base with tube connectors. New connectors are far stronger.

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[Dx G]

Robert - I don't know if you plan to have this dome exposed to beating sun or temperatures above 75.  Conduit in particular can get pretty hot in the sun. Most tapes become sticky gooey messes and then start to slip.  Instead of gripping, it would be like greasing the wires.  If you have experience to the contrary, than likely not a problem, but I know people who have wrapped old tool handles with tape, and yuck, a little heat and sweat and they won't do that one again.

DxG 

[Ashok Mathur]

Dear Robert

It’s a child play to cut good quality bamboo

 poles of 15 to 18 feet length.

So we could make dome of 45 to 54 feet

 diameter using bamboo poles that cost 

about   a dollar each in India.

If you made metal connectors that did not

 drill holes but just gripped each pole with 

a free rotating axis between the two grippers

We would have structure that would give good 

service before the  bamboos were eaten by bugs.

Regards

Ashok

Sent from my iPhone

On 06-Nov-2023, at 12:08 AM, Charles Lasater <charles...@gmail.com> wrote:



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<20231028_163352.jpg>

<20231028_163407.jpg>

[Travelling Telescope]

In addition to Ashok's words, you can treat bamboo very cheaply with salt (or slightly more expensive with a borax and boric acid solution) and the dome can last many years. Our dome is now 4 years old and showing no sign of insect damage. 

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[Eric Marceau]

I would have to second DxG's comment about tape and heat.  I wouldn't choose something that "iffy".

Eric

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[Robert Clark]

A lot of great feedback and ideas!  Here's another idea:  metal p-clamps attached by a panhead screw and nylok nut with a self-tapping screw thru the p-clamp to help keep it from slipping.

[Dx G]

You might find Paul Robinson's Wangers of interest if you had not seen it before. Its a pretty simple device, but if you look at his YouTubes, you will see the design took more sophistication than one might assume.  Although it is set up to use strut ends, it can be used further down the tube with some enhancement.  Not suitable for virtually everything, but the applications have a lot of range, especially for model and prototype work.

https://www.wangerflange.com/

DxG

[Levente Likhanecz]

the PVC star dome originally:

 https://www.stardome.jp/index-en.html

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[Dx G]

I don't know how far back the StarDome goes in Japan, but I've seen two different versions of this in dome books and publications going back to the 1960's.  I don't know when or where it began, although I suspect that several people have published their own version.

DxG

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[Robert Clark]

I'm curious if the star dome is in the category of reciprocal domes.  What exactly is the definition of a reciprocal dome structure?  Can a geodesic dome be considered a reciprocal dome?  Sort of like a square is a rectangle, but a rectangle is not always a square?

Just for more viewing interest, here's my version of a reciprocal dome next to Hiroshi Murata's Da Vinci (reciprocal) dome.

[Dx G]

One difference I see is that yours has rectangle/kite shapes, whereas his seem to be strictly triangles and pents, which is more what I've seen posted by Taff.  There may be some structural stability/strength issues unless diagonals are placed in your arrangement.

DxG

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[Levente Likhanecz]

as i recall, adrian's antiprism can calculate such design,

only i don't find the example on his website.

cheers, levente

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[Levente Likhanecz]

correction, i found it:

https://www.antiprism.com/examples/200_programs/705_rotegrity/rotegrity_pol8__Med.jpg.4.html

On Wed, Nov 8, 2023 at 5:33 PM Robert Clark <clark.rob...@gmail.com> wrote:

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[Robert Clark]

Dx G,

One would think that the rectangles seen in my reciprocal dome would cause stability issues.  That was my thought also when I first drew the design on paper.  But, as you look closer, there are many interconnected triangles that make the structure completely rigid and stable.  I could see this first hand as I assembled the model.

Robert

[Levente Likhanecz]

[Adrian Rossiter]

Hi Lev

On Wed, 8 Nov 2023, Levente Likhanecz wrote:
> as i recall, adrian's antiprism can calculate such design,
> only i don't find the example on his website.

I posted how to make Robert's (spherical) model here

https://groups.google.com/g/geodesichelp/c/HCkAd-2-BaY/m/TPHYfmRSBgAJ

The other model (as a sphere) can be made with

rotegrity -O r geo_3 | antiview

[Levente Likhanecz]

hi adrian,

thanx, i knew that your program is doing such  things, just i was looking the wrong corners.

cheers, lev

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[Charles Lasater]

I have built these DaVinci domes and what I like is all the vertical struts at the perimeter. Unlike yours it uses 4 different lengths.

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[Adrian Rossiter]

Hi Lev

On Wed, 8 Nov 2023, Levente Likhanecz wrote:

> On Wed, Nov 8, 2023 at 6:51 PM Levente Likhanecz <likh...@gmail.com> wrote:
>> correction, i found it:

In case it is of interest...

The model you posted appears to be the zonohedrification of a snub
dodecahedron with icosahedron vertex directions (!)

zono -S snub_dod -u ico | antiview

[Levente Likhanecz]

thank you.

i got addicted to the 4V kruschke, because of the simplicity, like the japanese stardome

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[Levente Likhanecz]

the 4v kruschke off file wrong, because not unit radius

off_color -e J 4vunit.off | antiview

On Thu, Nov 9, 2023 at 11:08 AM Adrian Rossiter <adr...@antiprism.com> wrote:

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[Robert Clark]

Just playing around some more with the rotegrity design.

It's modeled as a 16 diameter sphere with 2x4 wood struts and metal brackets, 3/4" bolts.

This version's style was inspired by O2Treehouse.com treehouses.

[Eric Marceau]

Thank you, Robert,

for what is clearly the result of a work of dedicated passion and intelligent creativity!

I would venture to say that it is a work of art!

(... and about now, my engineering DNA kicks in ...)

To you and to others devoting both your intellect and your creative juices to rotegrity design:

(very earnest questions)

• Is it practical to design/construct such a "complicated" structure? (admittedly skewed question)
  
  
• Comparatively, is it easier/simpler to design/build than the traditional "triangular geodesic grids"?
  
  
• Can a desirable "foundation plane" be easily identified, or are there limited (overly restrictive?) choices for the placement of such a plane?
  
  
• Is an arbitrarily chosen plane possible via control (direct relationship to) the sizing of the individual "panels"? 
  
  
• Do those panels maintain a fixed relative size in the overall pattern, or do some vary differently from others?
  

My questions stem purely from curiosity standpoint, looking to understand the underlying structure in "nature", with no motivation toward solving a problem or trying to use the approach for a build.

Thank you in advance for at least reviewing and considering my questions.

Eric

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[Robert Clark]

I agree.  It is admittedly a complicated structure with questionable practical use.  Boxes are not as interesting or organic looking, however they are simpler and make more efficient use of materials that are mostlly produced in rectangular and block form.  That is why we live in a world of boxes.  We sleep and eat in boxes. We go to work in boxes.  We study in boxes.

Robert

[Eric Marceau]

Hi Robert,

I am on the same wavelength as yourself, regarding the world of "boxes".  

Which is why I wish people would give more thought to micro-homes, and especially actual communities made of such homes, instead of over-engineered concrete bunkers being offered as condo/appt complexes, thereby making the unit cost per square foot/meter multiples of what it needs to be!

Concrete-mix maker-built (3D-printed) homes

• https://www.youtube.com/watch?v=20jovj6IHcw
• https://www.youtube.com/watch?v=utvm9B6ghh0

is another technology that has emerged over the past decade but, government/industry are myopic with their preconceived notions of what a house needs to look like or how it is to be built.

... and on this point, has anyone given thought to the possibility/feasibility/desirability of geodesic/tensegity structures built in-situ as maker-built structures ?

Eric

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[Robert Clark]

I am not trying to solve the problem of affordable/sustainable housing.  I'm not that smart and don't have an interest.  What interests me are quick to assemble, pop-up dome structures for storage, backyard studios, garden arbors, urban chicken enclosures, etc.  I'm attempting to create fanciful solutions to mostly non-existent problems of the first world.

[Charles Lasater]

I have been using 3/4" rigid EMT in a similar fashion.  Not very organic but makes a sturdy frame and the ends are malleable for connecting. Kind of a geo-rotegrity hybrid. 23' dia 13+ft ht. 400+ sq ft.

Parachutes make suitable shade coverings.

I enjoy your creative efforts.

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[Dx G]

We have some 3-D printed neighborhoods under construction in our region.  The idea is to get the cost of home construction down, and even allow construction to continue when human crews would normally not be working, such as under poor outdoor conditions or even in the dark.  The thinking has been the cost will come down as the system is improved.  Its also being eyed as a means to create more low cost housing and even provide shelter for the homeless.  Part of the problem is that people want the housing to look like existing housing, despite the fact that 3-D printing can be simpler and faster making something like a dome, rather than traditional rectilinear housing.  In fact, the current 3-D printer cranes are being designed to accommodate complicated or "fancy" house floor plans, whereas dome printing has no need for that level of sophistication.  So it seems to me the whole system, as well as the product, would cost a lot less for domes.  

    Using local materials, like soil, has a lot of advantages.  Cost of shipping a heavy raw material (concrete) which uses a high carbon footprint material (Portland Cement) is reduced or eliminated.  Whether it is *better* or not depends on what down sides there are to using native local materials.  The system would have to be robust enough to accommodate the amount of variation one can expect from one place to another.  In any case, I am hoping that technology advances in order to bring such housing/building options into reality.  I am glad to see its happening.

DxG

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[Ashok Mathur]

Dear Eric

Having built many rotogrities and domes 

also, I can say building a rotogrity is much 

simpler and harmonious.!

This is because there is symmetry and pattern

that yield a rhythm and harmony in the building 

process.

There are only two /three struts.

If you make up a rule that the left 

end of all struts will always be on the top of 

another strut, the pentagons, triangles and hexagons

 get easily made. You need not tighten the screws

fully in the first instance.

You can build the pentagon and the triangles

associated with it and then tighten all the screws.

The first rotogrity you build will be difficult.

That is because your brain and muscles are not

Yet seeing the patterns.

Start with a pentagon and add a visual number to 

to each strut so that you can check your progress.

Others may have even better techniques.

Regards

Ashok

Sent from my iPhone

On 27-Nov-2023, at 3:52 AM, Eric Marceau <eajma...@gmail.com> wrote:



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[Ashok Mathur]

Dear Eric

The answers below are not based on experience.

From the work of others, I would say finding truncation

 planes is not easy nor practiced.

An  Uneven truncation plane is supported by varying vertical stilts.

 

As every strut get divided into three equal parts, most panels have

 very similar dimensions and a penal approach looks possible.

Regards

Ashok

Sent from my iPhone

On 27-Nov-2023, at 6:06 AM, Charles Lasater <charles...@gmail.com> wrote:



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<moon ribs.jpg>

[Dick Fischbeck]

Another big part of the problem is land, not that there is a shortage of it, but, even when it is allowed, no one wants to be liable. I guess I don't blame them.

[Ashok Mathur]

Dear Eric,

Here is a picture of a rotogrity on vertical stilts of varying lengths.

The picture of a bamboo rotogrity without stilts will send a little later.

Regards

Ashok

[Eric Marceau]

Thank you VERY much, Ashok,

for addressing my various points directly.  That was informative and very much appreciated.

[1] From your first response, (I would only "hand-tighten" joints until all components were in place) is the pentagon the basic form at the apex of the structure?

[2] In the below picture, provided by you, I only see 1 size of vertical "stilts" for the foundation plane.  Is there something that I am missing?

[3] Also, are the various stilts steamed and formed with a curve, to facilitate assembly, before being incorporated into the structure?

[4] Lastly, I keep hearing references to bamboo being used for various structures.  Presumably those are "laminated" slats, like plywood.  Is that because bamboo has some inherent properties of resistance to moisture and mould?

Eric

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[Charles Lasater]

Rotegrity parachute greenhouse. 2 yrs old

3/8" digger pine slats  25' dia 35' parachute

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[Robert Clark]

This is what I'm talking about!!!!!!!  That is just awesome. Can you tell me what 3/8" digger pine slats are and where to get them?

[Dx G]

How does that do in the wind? We get 30-50mph winds here, sometimes for a whole day or more.  Domes are aerodynamic,  so usually do better than box structures.  Then there is snow load too, as it really gets heavy when it rains in the winter on top of snow, which acts like a sponge and the weight goes up fast. 

thx  DxG

[Charles Lasater]

3/8" plywood siding ripped into 3" strips works okay. A local farmer sawed up the pine strips for me but plywood doesn't have as many knots or weak spots. I used 5/16 Chicago screws (male and female).

Keep it up, Robert. Dome frames are satisfying.

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[Charles Lasater]

Surprisingly sturdy. We get big winds here. I used t posts to hold it down. Ultraviolet gets to the parachute after a few years.

To view this discussion on the web visit https://groups.google.com/d/msgid/geodesichelp/8b3a32cc-d657-43f4-959d-b08a066d786an%40googlegroups.com.

[Ashok Mathur]

Dear Eric 

Point wise reply follows

1. Read my sentence as half-tighten and not hand-tighten.

In a rotogrity, all vertexes consist of two struts crossing over each other.

So there is no pentagonal hub or a hexagonal hub.

I prefer to start with a pentagonal structure though you could start with a hexagon if they exist in the rotogrity.

2.All stilts are vertical and of same length within each truncation that I have seen.

Is it possible to have truncations where vertical stilts are different?I cant answer that question.

3. In rotogrity, there is no pere-bending of the struts. As the structures forms, the struts get naturally bent.The bending causes upward and downward forces that stabilize the structure.

4.You may be completely mistaken as to why bamboo is used. First I have not seen any laminated bamboo struts being used. Either natural bamboo poles are used or they are cured bamboo poles. Curing is processing increasing the structural life of a bamboo pole by preventing borer insects from eating it.

If you enjoy making models, try to make the simplest rotatgary with just 30 equal struts.

Regards

Ashok

Sent from my iPhone

On 28-Nov-2023, at 2:14 AM, Eric Marceau <eajma...@gmail.com> wrote:



Thank you VERY much, Ashok,

for addressing my various points directly.  That was informative and very much appreciated.

[1] From your first response, (I would only "hand-tighten" joints until all components were in place) is the pentagon the basic form at the apex of the structure?

[2] In the below picture, provided by you, I only see 1 size of vertical "stilts" for the foundation plane.  Is there something that I am missing?

[3] Also, are the various stilts steamed and formed with a curve, to facilitate assembly, before being incorporated into the structure?

[4] Lastly, I keep hearing references to bamboo being used for various structures.  Presumably those are "laminated" slats, like plywood.  Is that because bamboo has some inherent properties of resistance to moisture and mould?

Eric

On 2023-11-27 00:21, Ashok Mathur wrote:

Dear Eric,

Here is a picture of a rotogrity on vertical stilts of varying lengths.

The picture of a bamboo rotogrity without stilts will send a little later.

Regards

Ashok

<image.png>

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[Eric Marceau]

Thank you again, Ashok.  Very much appreciated!

Eric

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[Robert Clark]

Update to rotegrity sphere.  I 3D printed parts to create a plastic snap together model of my version of the rotegrity sphere.  It uses just one strut part repeated multiple times to create the sphere.  There are only 2 numbers needed to create your own models.  These are:  38.04835101 degrees and 7.74335271 degrees.

[Алексей Ярцев]

Robert, THIS IS GREAT.
I want to repeat this in metal.
Diameter 6 meters
I can set the required diameter of the arc for the workpieces on a pipe bender. Cut the blanks to your size and connect the parts together at the ends. The result will be a perfect sphere.
Question... what is the length of one sigmet of the structure? Is the total number of segments 120?

воскресенье, 26 ноября 2023 г. в 19:20:06 UTC+2, Robert Clark:

[Robert Clark]

Алексей,

Here are the dimensions you would need for a 6 meter diameter model:

 

[Dx G]

Robert,

  A question for you. Perhaps you already answered this at sometime in the past, but I missed it.  Taff posted a series of rotegrities made from 1, 2 or more chord lengths.  So what is the advantage of your model over the one he posted that is also entirely made of one chord length, all of identical size and hole pattern (4 holes)?  

thx DxG

[Robert Clark]

Hi Dx G,

The only advantage, I suppose, is that instead of two different strut lengths, my reconfiguration has just one.

Robert

[Paul Kranz]

Robert: Are those golden rectangles on the right-hand drawing? Paul sends...

To view this discussion on the web visit https://groups.google.com/d/msgid/geodesichelp/e58c52bb-7c46-436d-9b33-f9506875cf98n%40googlegroups.com.

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Very high regards,

 

Paul C. Kranz, LMFT

Kranz & Associates, LLC

ReviveTheFlame.com

[Dx G]

Robert,

 Actually, there is a rotegrity in his "catalog" that only uses 1 strut size, rather than two, referred to as a "one frequency".    Perhaps you had not seen that one.  I will attach it here.  It only has one strut length and only one distance between holes, so all struts are identical with uniform in hole distances, which simplifies fabrication. 

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[Robert Clark]

Hi Paul,

I was wondering that about the rectangles, also.  Golden rectangle is 1:1.618 and these are 1.957.  Also, it is slightly rhombus shaped, not quite rectangular.

And, to Alexey, I meant to confirm that yes, there are 120 struts in a full spherical model.

Robert

[Robert Clark]

Dx G,

Yes, I had seen that rotegrity that has just one strut length. I believe that is a smaller and simpler structure, however, with just 30 struts, not 120.

Robert

[Алексей Ярцев]

Robert, thanks for the answer) I have already made a table with the calculations. Your calculation and my calculations are the same.
Thank you, everything is described in great detail. This helped me!
I want to clarify.... I will not assemble a full ball/sphere with a diameter of 6 meters, but a truncated sphere Part of the sphere "on legs".
Nov 26, 2023 you called it Just playing around some more with the rotegrity design. This version's style was inspired by O2Treehouse.com treehouses . I'm delighted with your model!

Can I get the number of structural elements from you?
I understand that this model uses 2 types of elements (main elements and shorter elements that are installed at the bottom of the model)
How many main and additional elements?
I need to calculate the total amount of material for construction.
Best Regards, Alex

четверг, 21 декабря 2023 г. в 17:59:19 UTC+2, Robert Clark:

[Robert Clark]

Алексей,

The 3/4 dome you are refering to has 90 full struts (red & green), and 10 shortened struts (light blue) at the bottom.

[Алексей Ярцев]

Robert, thank you. I'll definitely show you the result BR Alex

четверг, 21 декабря 2023 г. в 21:07:52 UTC+2, Robert Clark:

[Ashok Mathur]

I have made several models of 1 frequency rotogrities.

They are simple to make.

Regards

Ashok

Sent from my iPhone

On 21-Dec-2023, at 10:40 PM, Алексей Ярцев <vipsw...@gmail.com> wrote:

Robert, thanks for the answer) I have already made a table with the calculations. Your calculation and my calculations are the same.

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[Robert Clark]

Here's an easy to build version of my rotegrity sphere.  It uses 3/4 inch plastic pipe hanger strap (Home Depot) held together with #4-40 x 1/4 inch long pan head screws (McMaster Carr). 

Cut the straps to lengths each containing 6 holes (4-1/2 inches long). You will need a quantity of 120 strips and 240 screws (and 240 nuts).  Place all the strips into near boiling water for about 30 seconds to relax the curl in the plastic.  This will make the strips much easier to work with.  The resulting rotegrity sphere is approximately 12 inches in diameter.  Instead of screws, you might use pop-rivets or Push-In Keyhole Shank Rivets (from McMaster-Carr).

-Robert Clark

[彭建宗]

你好，可以给我胶合板穹顶的图纸么？

在2023年11月4日星期六 UTC+8 09:59:57<Robert Clark> 写道：

I'm finally building a 24" diameter physical model of my design using bamboo strips and 2-56 size screws.  It's a nexorade that consists of just one strut type repeated throughout. Despite having rectangular features, the structure is rigid do to the triangular components.  120 bamboo struts create a full sphere held together with 240 screws.

[Ashok Mathur]

Dear  Zong,

Please forgive if I have your name wrong.

Wonderful work.

But Taff's nexorade uses 2 different struts  and the structure next to it uses 3 struts, 

How did you find a single strurt length and how is it divided into 3 parts?

Regards

Ashok

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[Robert Clark]

Ashok,

The structure next to Taff's doe not use 3 struts. As I designed it, it only uses 1 strut.

I recently got a Bambu Lab A1 3D printer and have been having fun playing with it.  I created the parts for my 1 strut nexorade (reciprocal dome) using TPU 64D filament.

Robert

[Ashok Mathur]

Dear Robert,

Wonderful pictures of  3d printed parts.

I misunderstood the 3 lengths in the black and white picture to mean 3 sizes of struts.

Now I am interpreting them to be the internal division of a single strut.

Now the only unknown is the ratio between the strut length and and the radius of the dome?

Is it (0.264482 +.135147 +o.264482) =0.66411 is the length of the strut and radius is 1.50577.

These suggest that they are not from geometry but were originally arbitrarily chosen and just fine tuned to make sure that the 90 degree angle is just that ?

So is there an intuitive way to think about nexorade?

Regards

Ashok

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[Robert Clark]

Ashok,

(0.264482 + 0.135147 + 0.264482) = 0.664069 length outer holes center to center for a 1.0 radius. That's a ratio of 1 : 1.5058.

These are exact geometric dimensions that exactly give a radius of 1.0.  No other dimensions will work. The results were found using parametric geometrical constraints in SolidWorks. It's quite a bit of tricky 3D modeling and took me many attempts to find a modeling solution that worked. At first I wasn't even sure if there were a solution.

Robert

[Dx G]

Robert,

 I'm not sure if Zong is his name, but he posted the drawing of the Taff nexorade made from one strut.  On first glance, his dimensions don't match yours, but seems like they provide the same result.  Perhaps there is something additional I'm missing.

Dx G

[Ashok Mathur]

Dear Robert 

Thanks for the clarification.

Regards

Ashok

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[Robert Clark]

Dx G,

Peng Jianzong simply uploaded a picture of my project that I had posted a while back. 

He said, "Hello, could you please provide me with the blueprints for the plywood dome?"

I guess no one remembers me posting it, it was that interesting (s/).

[Dx G]

Robert,

 I suspect we are not talking about the same image. I was referring to what he posted  Dec 16, 2025, 9:39:45 AM.  You will see a green/pink image of the single strut size unit by Taff. That's the one I was asking about.
thx Dx G

[Robert Clark]

Sorry, my mistake. I'll stay out of this.

[Robert Clark]

Actually, I'd like to clear up something about my 1-strut Rotegrity design.

Clarification on Stability of the Reciprocal Structure

A few comments have focused on the apparent rectangular (or kite-shaped) openings and whether they imply structural instability. I’d like to clarify how stability actually arises in this system.

• The structure is assembled from identical struts forming only two sub-assemblies:

  • chiral triangles

  • chiral pentagons

• Triangles are inherently rigid and have no internal shear degrees of freedom.

• Pentagons, in isolation, are not rigid and can rack if unconstrained.

• During assembly, each pentagon is stabilized early by the attachment of just two adjacent triangles.

  • Once those triangles are attached, the pentagon’s shear mode is eliminated.

  • At that point, the pentagon becomes a locked structural unit.

• The structure grows by repeating this same process:

  • an initially unstable pentagon

  • becomes rigid through attachment to already-rigid triangles

  • and then participates in stabilizing neighboring pentagons

• This is constraint propagation, not panel triangulation.

  • Stability emerges from the connectivity of members,

  • not from the visual shape of the voids.

• The rectangular or quadrilateral-looking openings are not structural frames.

  • They are residual gaps created after all local degrees of freedom are already constrained.

  • No load path depends on those voids resisting shear.

• Structurally speaking, there are no free quadrilateral degrees of freedom anywhere in the assembled system.

  • All potential shear modes are eliminated by member interlock before the global form is completed.

• Although the triangulation is not visually explicit everywhere, the structure behaves as a fully constrained network once assembled.

In short:

• The apparent rectangles are a visual artifact, not a mechanical one.

• Stability does not depend on the shape of the openings,

• but on whether degrees of freedom are constrained — and in this structure, they are.

[Dx G]

Robert,

  Actually, my question was about the data you posted Dec 16, 2025, 8:49:10 PM.  

You both show single strut nexorades, and I wondered if there was some fundamental difference between them that you were already aware of.

( On first glance, his dimensions don't match yours, but seems like they provide the same result. ) 

Any thoughts you have to share on that would be welcome.

thx Dx G

[Robert Clark]

Dx G,

I'm confused when you say, "You BOTH show single strut nexorades". As you see in the image, Taff's is the standard 2-strut nexorade (requires 120 total struts). And, just to the right of it is my 1-strut nexorade (also, requires 120 total struts).

Taff's dimensions are different because it is a different design. They are both nexorades, each constructed from 120 struts. The difference in designs is that I found a way to optimize and use just one unique strut instead of two. You know, doing more with less.

I hope this clears up any confusion you are having.

Robert

[Ashok Mathur]

If you carefully compare the zoo g photograph and Robert Clark’s photographs, soon you will realise that there are two different structures  that use simulate number of identical structures.

I wil try to make the differences clear after I have cut out  the photos.

Regards

Ashok

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[Dx G]

Robert,

 Yup, I sure fouled that one up.  You are entirely correct, the picture I referenced has two chord factors, not one.  So let's hit the reset button on the question.  I was thinking one thing and said another.

Your model shows a single strut as (0.264482 + 0.135147 + 0.264482) = 0.664069 (120  1-strut). However, I am aware of two other 1-strut length nexorades which I have on file. 

   If I'm reading it right, I see these:

1) By Taff  (.456158 x 3) = 1.368

2) By Adrian from Antiprism, which looks like (not sure) (0.150764 x 3) = 0.452291949677921;  sphere has 90   1-struts

I may be missing something important here, which is why I was asking.  Clearly the one you present has useful properties, although unlike the others, the hole spacing is not uniform (?) like they are with #1 above, and perhaps #2 (I have not verified or made model yet).

So what I originally meant to do was get your take on the assets and demerits of your model vs. the other 1-strut nexorades.  Could be I'd discover that if I looked more closely, but have not done so yet, and thought maybe you already had.

 Also, nice job on the Clarification of Stability.  It's useful to have that all organized and laid out.

 Perhaps Ashok will see this, so I will appreciate the results of his deliberations.

[Robert Clark]

The 2-strut dome was partially a product of arbitrarily deciding that all the holes should be evenly spaced. When I came to the conclusion  that there was no necessity for that constraint of having equally spaced holes, I was able to eventually reach the solution for the 1-strut, 120 piece nexorade.

Lower strut counts makes it easier to achieve 1-strut AND have holes evenly spaced.

One of these days when I have time and the weather is nice, I'd like to cut some 1/2" plywood into strips and and put together a quick 22.5' diameter dome. Unassembled, the strut slats would form four 8' long stacked piles 15" tall each. None of the parts have to be marked because there's only one part! Easily transportable by van or hatchback. When assembled and covered with tarp or plastic, would provided storage or work area out of the rain.

[Dx G]

Robert,

 A few thoughts to share -

Having evenly spaced holes does offer one possible advantage.  In terms of lowering material cost and reducing need for custom machining (along with any associated fabrication errors), its a lot easier to crank out strips or straps of continuous lengths if all the production requires is evenly perforated material.  One can even use perforated material made for something else, as long as the holes are compatible with the target distances needed, ignoring the holes in between.  As an example, there are some really good galvanized steel straps (various thicknesses and widths) made for hurricane/earthquake reinforcement of wood frame housing that come in rolls. All one needs to do is cut to size and bolt together through the holes the strips already have.

Second, nexorade #2 only has 90 struts, and both #1 and #2 are 1-strut domes.  So I was trying to dig up any reasons, other than those you already stated, that the 1-strut, 120 strut design you presented would be a better choice.

thx 

Dx Gl

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[Levente Likhanecz]

lately Adrian's rotegrity tool able to calculate with straight pipes. declaring drilling angles as well for all holes.　

if you go with standard pipe size it has fixed spherical radius for a given geo-modell

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[Robert Clark]

Dx G,

> One can even use perforated material made for something else, as long as the holes are compatible with the target distances needed, ignoring the holes in between.  As an example, there are some really good galvanized steel straps (various thicknesses and widths) made for hurricane/earthquake reinforcement of wood frame housing that come in rolls. All one needs to do is cut to size and bolt together through the holes the strips already have.

I did that with an earlier model of the nexorade. I used strips of perforated plastic plumbing pipe strapping. It had holes evenly spaced 0.75" apart. I was able to get it to work because the ratio distance in my design between outer and inner holes was a ratio of 1.95 : 1. That's close enough to the 2:1 hole pattern you could find on the strapping. See the image below.

Is 1-strut, 120 piece nexorade better than a 2-strut, 120 piece nexorade? Not really. It might be simpler to only have to deal with strut length and hole measurements for one strut, that's all. Other than that, it's just aesthetics preference.

Robert

[Ashok Mathur]

Dear Dx,

My reply is attached as a document. 

Both structures are identical.

Regards

Ashok

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[Robert Clark]

Ashok,

Argh! Yes, they are both identical. The thin, bamboo version and the black 3D printed one. 

Do you know why? Because they are BOTH mine (Robert, not Zong). Why is there so much confusion? LOL.

Zong was only posting a picture of my earlier bamboo version because he wanted to know the geometry dimensions.

This is becoming comical.

Robert

[Ashok Mathur]

Dear Robert

I am glad that this has berm sorted and credit belongs to you for figuring out the right answer!

Regards

Ashok

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