Is it feasible to make a dome out of a rotogrity?

[Ashok Mathur]

Dear All,

I have been making various models of rotogrities based on various models that Taff has placed in the library.

The closed models are quite strong.

Seeing one of the models made by me and comparing it with a twenty foot 4v dome , I find the rotogrity quite attractive  to make. Only 3 components cut out of thin strips.

What practical difficulties am I missing?

Is finding a truncation plane very difficult?

Regards

Ashok

Sent from my iPhone

On 28-Feb-2022, at 5:47 PM, Gerry in Quebec <toomey...@gmail.com> wrote:

The 3v dome cover diagrams and length lookup table on the Domerama website are for a dome using the Fuller-Kruschke subdivisiion of the icosahedron, not method 1. Hakim's dome appears to be method 1. 

- Gerry in Québec

On Saturday, February 26, 2022 at 8:54:31 PM UTC-5 you...@johnhurt.com wrote:

This link has some useful information:

http://www.domerama.com/calculators/cover-pattern/

John Hurt

On Thursday, February 24, 2022 at 5:40:31 AM UTC-6 lamtar...@gmail.com wrote:

Hello my friends
I built a 3v 5/8 dome
Spherical radius:303.754 cm
Spherical diameter: 607.509 cm
Height: 356,000 cm
I would like to cover the dome with a PVC canvas, I want to know exactly the distance surface measurements of each gore.
My PVC and 150 cm wide
thank you

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[Levente Likhanecz]

Dear Ashok,
what came to my mind looking at the Kruschke domes 3V, 4V, 5V-4planes
that each consist of "unbroken" arcs either great circles or lesser
circles.
and next the japanese bamboo stardome (
https://www.stardome.jp/index-en.html ), which built from great circle
arcs.
i guess those kruscke domes possible to build similar way.
there are PE (black-blue) plastic pipes (
https://www.ontozocentrum.hu/262-home_default/kpe-cso-25mm-6bar-pn6.jpg
)sold in coils of 100-200 meters.
just drill holes at the vertices along the arcs.
i attached the 4V model to look at.
the orange arc is forming the equator, so its a greatcircle. as well
the red-yellow-yellow-red arcs as them the sides of icosa triangles.
the green-blue-green-cyan sequence is a lesser circle (repeated
pattern).
so cut the length of the full arcs, drill the holes, and splice them
to sphere / half sphere.

cheer lev

[TaffGoch]

Murata's rotegrity dome employs element rotations, optimized to produce vertical members at the equator (ground level.)

(Handy for door openings.)

To skin a rotegrity, flexible panels/fabric is required, because the triangles are not planar.

Taff

(aka, TaffGoch, David Price)

[Ashok Mathur]

Dear Taff and Lev,

Thanks for the prompt responses.

I have been looking into the material that could be used to make the dome say of twenty foot radius or even smaller radii.

There are two obvious candidates.

One is flat ms strips up to say 5 cm wide and 3mm thick. They are readily available in 6 meter lengths or so. They are usually not galvanised so will need pre-treatment for long life.

There is another MS cross section that is suitable for interweaving- TMT rebar that is extensively used in RCC construction. Very thin rods have great strength.

https://www.realispat.com/blog-inside/what-are-tmt-rebars

But holes can not be drilled in them/ will require more effort for the holes to be drilled. 

But these bars have excellent welding properties and are pretreated to resit corrosion or loss of strength. A thin cot of concrete will bury the framework inside.

Let’s push the idea further

Regards

Ashok

Sent from my iPhone

On 04-Mar-2022, at 7:59 AM, TaffGoch <taff...@gmail.com> wrote:



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[Levente Likhanecz]

hi Ashok,
steel rebars you may mark for 'vertices' (e.g. cable ties) then fix
them together with twisted wire twinings, as construction builders do.
there are wire twisting tools for that purpose, even motorized.(in
builders code i recall they are against welding, cause it lose
mechanical properties and weldings are good spots for galvanic
corrosion)
anyhow, if you cover it up with concrete, then the concrete friction
will maintain their position.
rebars are protected against oxidation by the high PH of concrete,
unless the concrete thin, and by aging (taking up atmospheric CO2 -
carbonating) loosing the high alkaline feature of concrete and around
reaching PH 10 (from the original PH 12 level) the rebars ready for
corrosion. (galvanized rebars cost more)

by the way, adrian has such a lovely rotegrity module in the antiprism
package. can calculate diameter, drilling schedule for straight pipe
rotegrities, change division, simple and dual geo models. as i
remember it has 'stripe' style command as well.

cheers, lev

[Levente Likhanecz]

maybe the twining wire called 'seizing wire'

[TaffGoch]

Ashok,

Also, see Ctrl+Zeta's rotegrity dome project:
Ctrl+Z Architecture
“Sorbole” – Urban garden

-Taff

(aka, TaffGoch, David Price)

[Ashok Mathur]

Dear Taff

Thanks for this. In the meanwhile, I saw your animation in the 3D warehouse where you show the relationship between a dome and a rotegrity and have understood how to convert a rotegrity to a dome.

I wish to convey my thanks and appreciation for the way the archives are kept.

I wanted to see all the threads where I had discussed shallow cap icosahedron.

Instead of using the appropriate keywords, I fired my name as the search term, and instantly I was taken back to a decade ago i.e. 2012 when I started to post in the group. Slowly I have been working up my way and have reached till August 2017. All threads are intact and very easy to read and copy out what I think is of long-term use to me.

In connection with my new project, a twenty-foot radius dome as a restaurant, I have two points to make.

Gerry had posted a spreadsheet for shallow cap domes of frequencies 2 to 4. For 4 frequency dome it shows that you use only 105 struts instead of 250 struts, which is big saving in material and labor. But as the floor radius is somewhat less, you need to input a higher radius to get get the correct (longer)lengths of the struts.

For some reason, the pictures that Gerry had inserted in the spreadsheet have moved from their original positions and are obscuring the 4V strut length data.

Can Gerry repost that spreadsheet or can it be corrected in the archive?

Secondly, Gerry had posted on Mar 28, 2017 another spreadsheet of a 3v dome that has a hexagon at the top. The pentagons do not have any struts in them and therefore make attractive window positions.

Can I get another spreadsheet for a 4v shallow cap dome with a hexagon at the top?

See another email I just sent outside this thread.

Regards

Ashok

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[TaffGoch]

Ashok,

I found this image years  ago, but haven't been able to find its source, or any other additional information:

Russian house-forum topic - "Round house"

Also, found this yesterday:

Reciprocal dome "Da Vinci" from plywood strips (Russian)

-Taff

(aka, David Price)

[Ashok Mathur]

Dear Taff

Thanks for the photos, especially the full sphere with an in-between floor.

By now I have seen rotogrity domes based on your calculations in all types of materials such as bamboo, wood, plywood and pipes.

An easy and rough guide that I have evolved is that the maxim dome diameter that you will get is about  4 times the strut length.

Regards

Ashok

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[Ashok Mathur]

Dear Taff

The first dome photo seems to come from a Russian site 

Dome Nexorade DaVinci (sunhouse.pro)

You will see much of your work  used without any acknowledgment.

Regards

Ashok

[Levente Likhanecz]

Dear Ashok,
Adrian's Antiprism package able to calculate rotegrities with great flexibility.
He has it for linux and for windows as well.
simple and dual versions, and not bond to 1/3 divisions only.
my favorite kind with strait pipes, with proper drilling schedule.
the attached pic is a geo_3_d dual model, result of:
rotegrity -a n,0.4 -c S -O n geo_3_d | antiview -v 0.006320497048300
-e 0.006320497048300

and the data result is:
rotegrity -a n,0.4 -c S -O n geo_3_d | antiview -v 0.006320497048300
-e 0.006320497048300
1 max_diff:3.924691400378951e-02
Final iteration (solved, test value achieved):
76 max_diff:8.777083671441752e-16

Result
------
Radius and range of radius valaues, followed by minimum strut length
to ensure contact, then three lines per strut type
1: strut_index_number (used for colouring), number_of_struts, strut_length
2: length_to_1st_contact, length_to_2nd_contact,
length_to_3rd_contact, length_to_4th_contact
3: angle_of_1st_contact, angle_of_2nd_contact,
angle_of_3rd_contact, angle_of_4th_contact
Lengths are measured from either end of the strut
Angles (degrees) are measured looking along the strut central line
from the white end (display with -c u), anticlockwise, from an outward
pointing zero angle.

radius: 0.006320497048300 (+/-0.000000000000000)
strut length from: 0.346248799963225
0 , 60, 0.4000000000000
0.0268756000184, 0.1422918666728, 0.2577081333272, 0.3731243999816
-169.92165229, -11.14172472, 11.25133145, 169.92165229
1 , 60, 0.4000000000000
0.0268996401353, 0.1422998800451, 0.2577001199549, 0.3731003598647
-172.41922138, -13.63634902, 13.74594052, 172.41922138
2 , 30, 0.4000000000000
0.0294490901589, 0.1431496967196, 0.2568503032804, 0.3705509098411
-171.92304557, -12.82788541, 12.82788541, 171.92304557
3 , 60, 0.4000000000000
0.0307764830211, 0.1435921610070, 0.2564078389930, 0.3692235169789
-169.55328902, -10.40267653, 15.57058807, 169.55328902
4 , 60, 0.4000000000000
0.0532392515353, 0.1510797505118, 0.2489202494882, 0.3467607484647
-171.39541341, -13.96196751, 13.96196751, 171.39541341

cheers, lev

[Dick Fischbeck]

Excellent.

I am thinking that someone could build this by eye. Eyeballing, not measuring. Just a thought.

[Ashok Mathur]

Dear Lev,

Thanks for this. 

I have been wanting for years to learn how to use Anti-prism.

I see that in the jpg there are five colored struts, Red, Yellow, Deep Blue, Light Blue, and Violet. 

But you had started with only 4 struts and the program has calculated only four lengths.

Has the coloring gone wrong?

Regards

Ashok

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[Levente Likhanecz]

Dear Ashok,
Adrian has an old school indexing fashion.
Starts with zero.
That is the 5th there.

cheers, lev

[Ashok Mathur]

Got that.
A more detailed reply is being drafted by me - rather a wish list.

Regards
Ashok

Sent from my iPhone

> On 23-Mar-2022, at 2:47 PM, Levente Likhanecz <likh...@gmail.com> wrote:
>
> Dear Ashok,

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[Levente Likhanecz]

Dear Mr. Fischbeck,
i'm counting on your randome method, for emergency sheltering as skin
over a stronger frame. so the strength of the available cover material
not that much cardinal to bear self support.
somewhere i've tried to describe a 'strutless' build method for 4V
kruschke half sphere dome, similar to the japanese bamboo stardome.
(from coiled up polyethylene irrigation pipe)

cheers, lev

On 3/23/22, Dick Fischbeck <dick.fi...@gmail.com> wrote:
> Excellent.
>
> I am thinking that someone could build this by eye. Eyeballing, not
> measuring. Just a thought.
>
> On Mon, Mar 21, 2022 at 10:10 PM Ashok Mathur <ashokch...@gmail.com>
> wrote:
>
>> Dear Taff
>> Thanks for the photos, especially the full sphere with an in-between
>> floor.
>> By now I have seen rotogrity domes based on your calculations in all
>> types
>> of materials such as bamboo, wood, plywood and pipes.
>> An easy and rough guide that I have evolved is that the maxim dome
>> diameter that you will get is about 4 times the strut length.
>> Regards
>>
>> Ashok
>>
>>
>>
>> On Tue, Mar 22, 2022 at 6:41 AM TaffGoch <taff...@gmail.com> wrote:
>>

>>> *Ashok,*

>>>
>>> I found this image years ago, but haven't been able to find its source,
>>> or any other additional information:
>>> [image: 1d8fec0750870a6591a2511574acc253.jpg]

>>> *Russian house-forum topic - "Round house"
>>> <https://www-forumhouse-ru.translate.goog/threads/146237/page-25?_x_tr_sl=ru&_x_tr_tl=en&_x_tr_hl=en&_x_tr_pto=wapp>*

>>> Also, found this yesterday:
>>> [image: landscape02-6.jpg]

>>> *Reciprocal dome "Da Vinci" from plywood strips (Russian)
>>> <https://dome--by-com.translate.goog/portfolio/landscape/landscape02/?_x_tr_sl=ru&_x_tr_tl=en&_x_tr_hl=en&_x_tr_pto=wapp>*
>>>
>>> *-Taff*
>>> *(aka, David Price)*

>>>
>>>
>>
>
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[Levente Likhanecz]

Dear Ashok,
i forgot to mention that the rotegrity command text output does
include a radius data, the strutpipe radius:

(this line): radius: 0.006320497048300 (+/-0.000000000000000)
you have to divide your selected build pipe radius with that
calculated number, to get what radius your dome will have.
e.g. a 1 inch structural steel pipe O.D. is 33.7mm
33.7 / 2 / 0.006320497048300 = 2666mm as dome radius
so, the rest of the strut lengths and divisions lengths must be
multiplied to that dome radius.

cheers, lev

[Ashok Mathur]

Dear Lev,

I believe that if you are trying to build a structure of 10 meters or 1000 cm radius, which is quite big, you can work with a precision of a milimeter to align placements.

With that in mind I took this table from antiprisim from Lev's workings

and did two things. First I multiplied it by the radius of 1000 and then confined the results to display only one place of decimal

A number of things become clear at once.

First, all struts are of the same length ie 800 cms.

Secondly, struts 0 and 1 can be treated as identical.

Thirdly, without much distortion, struts 2 and 3  can be averaged and treated as one.

Thus this can be built as a 3 strut rotegrity.

Eyeballing is possible.

Lastly this is not an efficient way of building a rotegrity as strut length is a high percentage of the radius.

I will post some lower frequency rotegrity by Taff where the ratio of strut length to radius is much lower.

Regards

Ashok

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[Ashok Mathur]

Dear Lev,

This is from a email by Taff Goch dated Jul 12, 2016, 9:02:39 AM from thread 

called New Nexorade/Rotegrity project

Notice that the length of the longest Nexor is about 0.39 times the radius which implies we can get bigger structures for the same nexor length.

This can be reduced to just two lengths that differ from each other.

Wish list in next mail.

Regards

Ashok

[Adrian Rossiter]

Hi Ashok

On Thu, 24 Mar 2022, Ashok Mathur wrote:
> With that in mind I took this table from antiprisim from Lev's workings
> [image: image.png]
> and did two things. First I multiplied it by the radius of 1000 and then
> confined the results to display only one place of decimal
> [image: image.png]
>
> A number of things become clear at once.
> First, all struts are of the same length ie 800 cms.

You don't appear to be interpreting the 'rotegrity' program output
correctly. If you look at your table the space at one end of unit 0
is 0.02... and at the other end it is 0.37...! In the program output
the length values are distances measured from one end of the strut.

Also, you seem to be comparing straight unit nexorades to arced unit
rotegrities with regard to a common sphere, but the nexorades tend to
vary from spherical, and this particular one varies by at least 1.2%,
so if you are comparing models directly then you would need to define
the sphere that corresponds to a nexorde model.

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

[Ashok Mathur]

Dear Adrian
As I had no experience of interpreting the out, I thank you for pointing out my errors.
I will get back to you after testifying the figures correctly.
On the second point , are you saying that in nexorades the struts are straight chords that dip up and under, while in rotogrity they are parts of spherical triangles that dip up and under?
Please be patient with me.
Thanks

Ashok

Sent from my iPhone

> On 24-Mar-2022, at 2:46 PM, Adrian Rossiter <adr...@antiprism.com> wrote:
>
> Hi Ashok

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[Adrian Rossiter]

Hi Ashok

On Thu, 24 Mar 2022, Ashok Mathur wrote:
> correctly. On the second point , are you saying that in nexorades the
> struts are straight chords that dip up and under, while in rotogrity
> they are parts of spherical triangles that dip up and under? Please be
> patient with me.

Avoiding the issue of what terms might be considered correct, these
seemed like commonly used terms for the different model types when
I wrote the 'rotegrity' program, and are the terms used by the
program: nexorades are made of straight rods, and rotegrites are made
of arced bands (and in the real world these bands have a thickness,
which affects the model shape, but slots could be cut into the
thickness where the units overlap to improve sphericity).

[Ashok Mathur]

Thanks for the clarification.
Regards

Ashok

Sent from my iPhone

> On 24-Mar-2022, at 5:24 PM, Adrian Rossiter <adr...@antiprism.com> wrote:
>
> Hi Ashok

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[Ashok Mathur]

Dear Adrian

Is this interpretation of the output correct? Radius is 1000 cms and output is displayed to the nearest millimeter.

My revised conclusions based on this are:

The design length of longest strut to radius is acceptable.

Struts 0 and 1 are identical and struts 2 and 3 could be averaged without  much loss of precision.

Now to my wish list based on a desire to play with nexorades as your programme encourages.

Some wish-list elements may already be present in Anti-prism; others may require additional programming.

Can I specify:

(i) a ratio of medium strut length  as a fraction of radius? So, can I input an additional parameter that the maximum strut length should not be more than 33% (0.333333) of the radius?

(ii) struts lengths may vary from each other till say 25%  of average length or shortest vs longest should not vary by more than 25%?

(iii)When I was doing LP programming, I discovered that examining the last five iterations often yielded a solution that was very easy to implement rather than the last optimised solution. In AI this practise has been called top five error meaning that if my AI engine makes a mistake, the correct answer should be in the last five guesses it made. Can Anti-prism have such a feature which is not difficult to implement?

Thanks for even considering this.

Regards

Ashok

[Adrian Rossiter]

Hi Ashok

On Thu, 24 Mar 2022, Ashok Mathur wrote:
> Is this interpretation of the output correct? Radius is 1000 cms and output
> is displayed to the nearest millimeter.

Almost. Lev ran the program for a common strut length of 0.4, which
is listed in the report, and if you add the first length to the
last for unit 0 you get 26.9 + 373.1 = 400.0

> Can I specify:
> (i) a ratio of medium strut length as a fraction of radius? So, can I
> input an additional parameter that the maximum strut length should not be
> more than 33% (0.333333) of the radius?

The program makes a nexorade from the base model based on the contact
point spacing. This determines the common rod radius and puts a minimum
length on a common rod length. If you want to optimise something then
search the solutions based on the contact spacing parameter.

> (ii) struts lengths may vary from each other till say 25% of average
> length or shortest vs longest should not vary by more than 25%?

Again, you could search for a solution with the properties you want.

> called top five error meaning that if my AI engine makes a mistake, the
> correct answer should be in the last five guesses it made. Can Anti-prism
> have such a feature which is not difficult to implement?

The rotegrity program iterates towards a local equilibrium solution.
It could iterate towards an equilibrium that is not of interest, or
there may be no equilbrium position (e.g. nexorade basedd on doughnut
surface). If the algorithm is converging on a solution then, generally,
the more iterations the better the solution. Try running the program
and vary the number of iterations to see what happens.

[Levente Likhanecz]

ohhh,
that was a 'dual' arrangement, which allows to build on much larger
diameter, than the simple model. (attached the not dual pic)
this method with that special radius number calculated for straight,
rigid (steel) pipes, that will just 'touch' each others at proper
drilled positions, without generating tension.
you might go below in pipe O.D., and the bolt and nut will pull them
closer, or apply spacers.

maybe you remember those university students, who built one from
massive, maybe 4 inch dia steel pipes for a science fair (i dont know
how to locate those pics from the group).
due to slight missizing they faced difficulties, to assemble it, dueto
high tensions.
guess the 4 inch steel did not want to bend on will.

my estimation, that the choosen pipe diameter rules the dome size.

for simplicity of the calculatios even length struts were selected.
someone may recalculate (excel), that all struts ends just ovarhang by
5 cm.

cheers, lev

> https://groups.google.com/d/msgid/geodesichelp/CAD-a3Og%2BiC8jj8u69-dz9fv_k%3DeKUqg25xW1b53kgU2j0n6Mbg%40mail.gmail.com.
>

[Adrian Rossiter]

Hi Ashok

On Thu, 24 Mar 2022, Adrian Rossiter wrote:
> the more iterations the better the solution. Try running the program
> and vary the number of iterations to see what happens.

Program documentation (whoops, spelling of nexorade)

https://www.antiprism.com/programs/rotegrity.html

Examples

https://www.antiprism.com/examples/200_programs/705_rotegrity/imagelist.html

[Ashok Mathur]

Dear Adrian,

Two problems.

First I can not find the stable version  0.28 windows 64 installer anywhere.

Second 0.29 windows installer's download is being blocked by Microsoft Smart Screen.

Are there work arounds?

Regards

Ashok

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[Adrian Rossiter]

Hi Ashok

On Fri, 25 Mar 2022, Ashok Mathur wrote:
> First I can not find the stable version 0.28 windows 64 installer anywhere.

The current release version is Antiprism 0.29

http://www.antiprism.com/download/

> Second 0.29 windows installer's download is being blocked by Microsoft
> Smart Screen.
> Are there work arounds?

If you specifically mean the download is being blocked, check if there
is an optione to confirm that you really want to download it.

If you are having trouble running the installer because I am an
"unknown publisher" then maybe you can click "Run anyway". Otherwise,
maybe this article will help

https://www.windowsdigitals.com/how-to-allow-unknown-publisher-in-windows-10/

If not, please give more details about what you are doing when the
warning appears, and the exact text of warning.