3 V Shallow Icosahedron Cap model and dome making

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Ashok Mathur

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May 14, 2026, 10:24:50 PM (9 days ago) May 14
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Dear List

 

Shallow Cap Icosahedron  domes - 3V truncated, leveled domes

 

I have been able to trace reference to above type of domes in the list from 2007 onwards. 

 

I initiated a discussion on a 3 frequency shallow cap geodesic dome with flat base on 9th April 2012 .There were many participants in the discussion, but Gerry and I were particularly interested in the subject.

 

On 26th April 2012 Gerry calculated and produced in a spread sheet the calculations for a shallow cap 3 frequency flat base dome.

 

On 26th December 2018  Gerry produced a spread sheet that also covers 4 and 5 frequencies geodesic domes.This detailed spread sheet can be downloaded from this link.

 

https://drive.google.com/drive/folders/1MtdCmvNu-krskwRZJEy9Ry7Mn2-LfVwz?usp=sharing

 

I was invited to teach Geodesic domes over  two day workshop to the students of architecture at  the College of Architecture at MMA Pune.

One day of the workshop would be spent on theory coupled with model making, Next day we would assemble an actual dome.

 

Because the 3V truncated leveled version of the dome saves about 40% of  all cost and is easy to build, I decided that this is what I would build with the students.

 

The dome would be 14 feet in radius and only 9 feet in height and would be made from struts fabricated from 33mm OD steel pipes flattened ends with holes for nut-bolt joining.

 

 On the first day the students would build 3 models, a 3V truncated, leveled, shallow dome, another model of the same dome with 30 inch raiser walls and finally a standard 3V 5/8 dome.  An idea of the first days working can be had from this You Tube presentation https://youtu.be/V0Y_9-uJnvI.

 

The second day the actual dome assembled in about 2 hours.Its presentation is here

https://youtu.be/QvfLFE92C3U

 

Regards

Ashok

 


Meparth singh rajput

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May 15, 2026, 1:44:13 AM (8 days ago) May 15
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Hi, I want to learn and analysis of geodesic dome 
Second, how i perform fea analysis in a dome? I choose a 3V dome of 5/8. Can you help me out? And also, how do i prepare a dom model in CAD software? Please help me this.

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Ashok Mathur

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May 15, 2026, 1:57:06 AM (8 days ago) May 15
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Dear Rajput
I am answering the second question first i.e. fea analysis of a geodesic dome.
I am one of very few members who believe that fea or fema are not good tools to analyze the strength of a geodesic dome. 
Both tools are based on a premise that the reaction to a force applied is very local and is confined to the spot where force is applied. However domes react as a whole and not just at that point. 
Secondly both tools assume that the constant of elasticity is just that. But experiments with a dome show that near the equilibrium point the constant of elasticity varies by five times from the constant value.
Thirdly domes rotate when a pressure is applied. Neither tool measures this aspect.

What you are asking in the first question is not clear to me.
Are you wanting a dome calculator, or you want to understand the theory of a tensegrity structure.
Regards
Ashok


Regards

Ashok




Ashok Mathur

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May 15, 2026, 2:05:15 AM (8 days ago) May 15
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Dear Rajput
I overlooked the third question that you have asked.
A student from UK was committed to doing a FEA analysis of the Pabal Dome. Despite my explaining the short commings of FEA and FEMA he wanted my help in doing this despite knowing the  answers represented simply mathematical calculations without any connections with reality.
I helped him beacuse he might get a fail grade otherwise.

Regards

Ashok



Ashok Mathur

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May 15, 2026, 2:15:00 AM (8 days ago) May 15
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Dx G

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May 15, 2026, 9:13:13 PM (8 days ago) May 15
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Rajput,
  If you do a search on "dome structural analysis", you will find quite a few interesting items.  There will be some overlap among them, but any any one will usually have analysis on a few things that are unlike the others, and often using different approaches.  Some have aspects of the analysis that discuss things you want to do.  Keep in mind that many of these did not verify their findings with physical models, so their conclusions may not be reliable.

 Here are a few examples of what came up initially:


Those should be good for a start but there are more.

Dx G

Ashok Mathur

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May 16, 2026, 12:48:02 AM (8 days ago) May 16
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Dear Rajput
If you have any professional interest in making Geodesic domes than upto 11 or 12 frequencies Cadre Geo gives solid help based on personal experience.

The second cited paper https://www.ijert.org/research/parametric-study-and-optimization-of-steel-dome-structure-IJERTV11IS080017.pdf has nothing to do with finding the strength of a dome. It considers what are commonly called trapieum domes and calculates the optium number of segments  for a given weight.As it uses no triangulation at all, it is not very relavent.

The third citation is good. To quote its purpose is "The purpose of this report is to present the background information about geodesic dome, also to verify a designing methodology and to develop design procedure based on the most critical loading, that is wind load for this type of structure. The aid of computational analysis has been considered as the key tool to obtain design data from the complex 3D dome model, and then manually checked against steel structure standards AS 4100-1998.

In addition, an Excel spreadsheet was developed using finite element analysis method to extract the forces for each element, then the results were compared against the outcomes from computational analysis method for validation purpose. The spreadsheet was aimed to standardize the design procedure and to reduce the time required for analysis and design in the future, and sensitivity analysis could also be conducted easily and quickly using the spreadsheet." Note that it does compare the computed results against any real tensegrity structures.

Page 40 of the report say the following "The model was analysed as a 3D space truss with its ground level nodes restrained for

lateral movement. Each member was treated as single element with two pinned end restraints, therefore, each member undergoes axial forces only"
So the analysis ignores response as a whole, twisting of the dome and change in constant of elasticity.
You are welcome to look up the balance of other reports.
Regards

Ashok




Gerry in Quebec

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May 17, 2026, 2:37:45 AM (6 days ago) May 17
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Thanks, Ashok. Good to see your efforts "on the ground" in India to promote geodesic domes. I really enjoyed your course-related videos. I'm also glad to see that old Excel spreadsheet of the icosa caps was useful.
Cheers,
- Gerry in Québec
(where the dreaded black flies of late May & early June  have just arrived)

Ashok Mathur

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May 17, 2026, 11:35:43 AM (6 days ago) May 17
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Very happy to hear from you.
Most likely I will teach North Nigerian farmers to build such domes as green houses. In that place green houses are built to keep the heat out and retain moisture!


Regards

Ashok



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Dx G

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May 17, 2026, 1:04:05 PM (6 days ago) May 17
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Ashok,
  If you are going to be working with greenhouses in a hot climate, let me pass along a few thoughts in case they might be helpful.

1) Firstly, as rule, without active cooling, usually the best you can do is prevent the inside of the greenhouse from getting warmer than the ambient air.  However, there are exceptions where passive methods can also.
 
 a) Typically refrigerated air conditioning is not used for greenhouses, but of course is an option

 b) A common cooling system used in greenhouse are "pads".  Usually water is dripped through an air permeable paper, aluminum (or other material) "pad", which functions like a radiator.  It can work well at low ambient humidities, less so at higher humidities, but less so or not at all at higher humidities.
    There are also stand alone "swamp coolers" that substitute for refrigerated AC units and work really well at low humidity, although consume water.

 c) Certain systems circulate water through the glazing to prevent heating with minimal loss in light intensity, but these are used more in greenhouse research and not often in more commercial settings.
  Alternatives would be a fine droplet spraying system that applies water to the roof surface to prevent heating, or the use of "fog" systems inside the greenhouse (available commercially).

 d) Geothermal cooling approaches could be a good option as a passive or powered system.  

 e) Some regions reliably have much cooler temperatures at night, and good use can be made of this to help prevent high temperatures during the day. Typically this is done using hollow masonry or stone passages as a heat exchanger, although water (typically a tank, pool, etc.) is much more effective than stone on a volume basis.


2) Passive methods - do not require energy input

 a) Rather than using clear poly for the cover, white poly can help reduce temperature a great deal. Typically there will be some reduction in light intensity. However, the reduction in temperature can be far greater than light intensity loss, especially in regions with high sun light intensity.
  Another commonly used method is spraying clear poly with a paint-like coating called shading compound. The applicator has some control over the level of shading desired by how much is applied. Usually this coating can be removed in a cooler season so that the poly does not have to be replaced.

 b) Venting at the top of the greenhouse with air intakes lower down can help prevent hot air buildup. Vents are available which automatically close/open at a temperature setpoint without any power source at all (further info available on request).
  We have had some discussions about the "chilling machine" on the list.  I reviewed this some time ago and have some doubts about the veracity of explanations I have seen about why it works.  However, clearly it does, and I think I see why. This leads me to suspect the system is highly dependent on the local weather, thus will work poorly or not at all under some conditions.  
   Blair was making a concerted attempt to deploy a chilling machine, so perhaps eventually we will hear more from him on the topic. The background work I did led me to suspect that in his climate, there would be some days it would work and others not at all.

I might think of a few more things, but wanted to pass these along in case they were not already on your radar screen.  In addition, I thought it might be of interest to others on the list.

Dx G

Ashok Mathur

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May 18, 2026, 2:00:46 AM (5 days ago) May 18
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Dear Dx

I am thankful for your detailed guidelines. Because the work I want to do in North Africa may be outside the interest of most members of the group, I will keep my replies brief and embed them in your response in a blue font.

 

Ashok,
  If you are going to be working with greenhouses in a hot climate, let me pass along a few thoughts in case they might be helpful.

1) Firstly, as rule, without active cooling, usually the best you can do is prevent the inside of the greenhouse from getting warmer than the ambient air.  However, there are exceptions where passive methods can also. 
 
 a) Typically refrigerated air conditioning is not used for greenhouses, but of course is an option

 b) A common cooling system used in greenhouse are "pads".  Usually water is dripped through an air permeable paper, aluminum (or other material) "pad", which functions like a radiator.  It can work well at low ambient humadities, less so at higher humidities, but less so or not at all at higher humidities.


    There are also stand alone "swamp coolers" that substitute for refrigerated AC units and work really well at low humidity, although consume water.

 

 c) Certain systems circulate water through the glazing to prevent heating with minimal loss in light intensity, but these are used more in greenhouse research and not often in more commercial settings. 
  Alternatives would be a fine droplet spraying system that applies water to the roof surface to prevent heating, or the use of "fog" systems inside the greenhouse (available commercially).


The above constitutes what is called passive evoprative cooling and is used on a massive scale in India and I am familiar with it from childhood.I doubt if I will incorporate this in my design . I would rather use canopy management and reduce leaves to the minimum.



 d) Geothermal cooling approaches could be a good option as a passive or powered system.  


Conditions in North Nigeria are like a hot dessert, which is next door and no Geothermal structures exist in the area.


 e) Some regions reliably have much cooler temperatures at night, and good use can be made of this to help prevent high temperatures during the day. Typically this is done using hollow masonry or stone passages as a heat exchanger, although water (typically a tank, pool, etc.) is much more effective than stone on a volume basis.


North Nigeria always has cooler nights than day the difference is considerable.



2) Passive methods - do not require energy input

 a) Rather than using clear poly for the cover, white poly can help reduce temperature a great deal. Typically there will be some reduction in light intensity. However, the reduction in temperature can be far greater than light intensity loss, especially in regions with high sun light intensity.
  Another commonly used method is spraying clear poly with a paint-like coating called shading compound. The applicator has some control over the level of shading desired by how much is applied. Usually this coating can be removed in a cooler season so that the poly does not have to be replaced. 


I will use a shading compound on poly. If the structure is made with bamboo and skills to make bamboo panels exist in the region, I will use bamboo panel as shades rather than poly.


 b) Venting at the top of the greenhouse with air intakes lower down can help prevent hot air buildup. Vents are available which automatically close/open at a temperature set point without any power source at all (further info available on request).

 

I will use vents at top. For bigger green houses, there are wind driven vents which use no electricity.


  We have had some discussions about the "chilling machine" on the list.  I reviewed this some time ago and have some doubts about the veracity of explanations I have seen about why it works.  However, clearly it does, and I think I see why. This leads me to suspect the system is highly dependent on the local weather, thus will work poorly or not at all under some conditions.  

 

My approach is this: A geodesic dome or a tunnel, is not the most important part of the solution- teaching farmers good Agriculture practices will give far more income to the farmers.

Brief bullet point wise good agriculuture practices involve.

Ensure non-expired VAM mycorrhiza is incorporate in the rooting soil.

Ensure planting soil has vermicompost, biochar, and VAM.

Use modified Root Feast methodology for underground wick irrigation.This system does not use a pulsating pressure pump, difficult to maintain filters etc but inserts terrycot material wicks in a drip pipe and feed the water and organic nutrients after sun set by gravity and capillary action.

Select the crop from a limited set of crops that can be grown like a vine on a trellis.

Leaves are your enemy; use canopy management to cut them away with disinfected sequencers

 

Blair was making a concerted attempt to deploy a chilling machine, so perhaps eventually we will hear more from him on the topic. The background work I did led me to suspect that in his climate, there would be some days it would work and others not at all.

I might think of a few more things, but wanted to pass these along in case they were not already on your radar screen.  In addition, I thought it might be of interest to others on the list.

Dx G

 

 

Regards

Ashok




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