Shallow Cap Icosahedral Domes

[Ashok Mathur]

Dear All,

Starting from year 2007 , there have been several threads in this group on the above subject.

For 3v shallow cap dome, Gerry had made a excel sheet where the base had been leveled by addition of a fourth strut.

My calculation show that despite the addition of a fourth strut, if the shallow cap icosahederal dome is compared with a leveled 3/8 3v dome. there are good economies to be had in both the total lengths of struts to be used in the construction and in the surface area to be covered.

I can freely share my calculations showing the savings but you will have to insert your own rates for the steel that you plan to use.

Recently a person has shown some interest in constructing a 40 foot diameter dome.

Such large domes require a careful approach, which in my way of understanding means a 4v instead of 3v construction.

Now a 4v dome sits leveled at 1/2 truncation.

I am not sure if it sits level at the shallow cap truncation.

My maths knowledge does not allow me to calculate this.

I am looking to Gerry in particular and anybody else who can help to give me an excel sheet for 4v shallow cap icosahedral dome.

Normally I use an angle iron which weighs about 1.16 kilos per running meter for 3v struts. (25mm x 25mm x 3mm Mild Steel Angle Iron)

For 4 v construction I am thinking to switch to 25mm x 25mm x 5mm Mild Steel Angle Iron that wighs about 1.7 kgs per running meter.

Regards

Ashok

[Gerry in Quebec]

Hi Ashok,

An Excel calculator for 2v, 3v & 4v icosahedral caps with a flat truncation is attached. Note that the 4v dome produced by this calculator has 9 chord factors. Maybe that number can be reduced.

Cheers,

- Gerry

[Ashok Mathur]

Dear gerry,

This makes for a wonderful Christmas gift.

I shall play with it and get back to you.

Thanks

Regards

Ashok

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[Ashok Mathur]

Dear Robert

Thanks for the prompt reply.

I have had a first look at your solution.

It is obvious that you have done a lot optimization to reach a solution with just four struts.

But the lengths of the four struts leave me a whole lot confused.

The diagram shows that the diameter of the dome is 33 feet.

The shortest strut is about 44 feet and the longest is about 65 feet.

Or I am reading the strut lengths wrong and the shortest is 0.44 times a unit radius and largest is 0.65 times the unit radius.

Even so these are very long strut and the total strut length of about 300 struts is going to be a very long length.

Please clarify what am I reading wrong.

Regards

Ashok

On Tue, Dec 25, 2018 at 7:08 PM Robert Clark <clark.rob...@gmail.com> wrote:

This 4V dome sits level at 3/8 and 5/8 levels and has 4 strut lengths.

On Tuesday, December 25, 2018 at 2:31:49 AM UTC-5, Ashok Mathur wrote:

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[Ken Brown]

In case anyone has missed this tidbit, an icosahedron that is orientated edge to top has a natural truncation plane at the equator. 

Ken G. Brown

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<Icosa-caps-Toomey.xls>

[Ken Brown]

Thx. Good to see the picture. 

Ken G. Brown

On Dec 31, 2018, at 06:40, Robert Clark <clark.rob...@gmail.com> wrote:

Ken,

Here is an icosahedron oriented with edge at top.  Two edges would sit flat on a truncation plane at the equator, but four of the triangle panels would have to be bisected.

Robert

<icosahedron-1.jpg>

[Paul Kranz]

Ken. That's what I was thinking in 1982 when I came up with the DoggiDome.

Paul sends...

[ashokch...@gmail.com]

Dear Gerry

In the previous post, Robert has posted a 4V dome with just 4 struts. 

Somehow in my head, there is an idea that you had derived this 4 strut structure. 

If it is a derivation of somebody else ( perhaps Robert himself), my sincere apologies..

Can these reduce variety of struts be used to make a shallow cap dome?

Regards

Ashok

On Wednesday, January 2, 2019 at 8:35:34 AM UTC+5:30 clark.rob...@gmail.com wrote:

Ashok,

In the first diagram I posted for a 33 foot diameter 4V dome, the shortest strut is 44 inches and the longest is 65 inches. Sorry about that. I'm not sure if you saw, but I had posted a reworked diagram that shows the strut lengths as a decimal fraction of a unit radius dome. Here is the diagram again. I should probably just use metric measurements to avoid confusion. Cheers.

Robert

[Gerry in Quebec]

Hi Ashok,
As I recall, Rob and I each came up with the same 4v icosa, 4-strut subdivision completely independently. About 10 years ago, I worked with  two customers in Vermont, USA, on the design of two domes, 20 ft and 50 ft in diameter, based on that geometry. Both domes were the tall version, 7/12 truncation. 

Here's a link to a photo:

https://groups.google.com/g/geodesichelp/c/jvI0f6HydUw/m/Bl6IzsJ_dwMJ

As you suggest, this subdivision can be used to make a shallow icosa-cap dome (base radius / height = golden mean = 1.618034) with one less strut length than the 4v icosa-cap presented in the Excel spreadsheet I posted.

- Gerry in Québec