Re: 5V class-I dome requiring only 4 different struts

[Hector Alfredo Hernández Hdez.]

Wow :)

2014-09-05 18:55 GMT-07:00 Robert Clark <clark....@verizon.net>:

5V class-I dome requiring only 4 different struts and 4 unique panels - all isosceles.

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[Hector Alfredo Hernández Hdez.]

gray are equilater and other isoseles, ok?

[Adrian Rossiter]

Hi Robert

On Fri, 5 Sep 2014, Robert Clark wrote:
> 5V class-I dome requiring only 4 different struts and 4 unique panels - all
> isosceles.

Do the vertices of this one lie on a sphere? (Looks like it is
short of a degree of freedom and would only happen by circumstance).

Adrian.
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[Gerry in Quebec]

Hello Rob,
Nice job on the triangle layout of the 5v icosa dome. Technically, there are 5 chord lengths and 5 triangle types, not 4, if I have understood your illustration correctly. But two of the chord lengths are so close in value they can be treated as equal for construction purposes. See the attached jpg. At a dome diameter of 50 feet, the difference in the two D-type strut lengths is about 1/16".

I have put together a few unconventional layouts of the 5v icosa, class I, one of which was used for a 42 ft greenhouse in Washington State, USA, completed about a year ago. It's a low-profile dome with a flat base. I'll dig out some pix and post them.

- Gerry in Quebec

On Friday, September 5, 2014 9:55:49 PM UTC-4, Robert Clark wrote:

[Hector Alfredo Hernández Hdez.]

thinking about our searchers with Gerry and Taff

I can pronosticate that is no posible to have less of 5 struts (diferrent) for frecuency 5.

(I found too a some inconsistence en the desing propososed)

at least you change some r=1 (exacly)...

what do you think about Gerry & Taff?

See you

PD: my doctoral studies are walking :)

2014-09-06 7:26 GMT-07:00 robert clark <clark....@verizon.net>:

Some of the vertices lie slightly inside and outside of the sphere.  This
little bit of cheating is how I could get the 5V down to just 4 struts.  If
this were a 24 foot diameter dome, then the vertices that did not lie on the
sphere would only be off .03 inches or the thickness of a credit card. See
the attached image for exact dimensions. -Rob

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[Hector Alfredo Hernández Hdez.]

Too let change radius is a great Idea for practical proposal.

Is time to put a perfect sphere on other pedestal :)

Gerry have desings like thats

[Gerry in Quebec]

Here are two examples of what Hector is referring to, i.e., domes with more than one radius length.

 

The first is a 5v layout that Hector and I worked on a couple of years ago (jpg image attached). It's similar to the design Rob posted yesterday because it, too, has only 4 chord factors. But I think Rob's design is better as it has fewer triangle types.

 

The second example is a 4v icosa, class I dome home in the Green Mountains of Vermont, USA:

https://groups.google.com/forum/#!searchin/geodesichelp/Vermont$20dome/geodesichelp/Gg32ZLBCpAk/cwGL4fp3k00J

 

The main dome, about 50 ft in diameter, has a double shell -- 2x6 construction outside, 2x4 inside. There is also a single-shell 20 ft dome, of 2x6 construction, same geometry.

 

A tiny increase in the length of the radii to certain vertices made the domes easier to build by reducing the number of strut lengths and panel types to 4 & 4. The design also allowed for a level base at the 7/12 truncation. However, none of the anomalous vertices occurred in the domes' bases, which made it easier for the concrete-foundation crew to stake out the footprints (same distance from the centre point to each of the 20 vertices of each dome).

 

- Gerry in Quebec

[Hector Alfredo Hernández Hdez.]

Roberto Clark: If you change a red strut by a green one.

you will have ONLY 3 L struts and a beatiful dome :).

[Gerry in Quebec]

Hi Rob,

The two wooden shells of the main dome, with a 14" gap for insulation, were raised independently. The owner-builder did all the compound cuts himself -- with lots of patience and some recutting of imprecise longer struts into precise shorter struts as he got the hang of it on the radial arm saw. Each triangle was then reinforced with 2x4 T-blocking and then the two frames were married by means of 12" x 12" OSB gussets.

Here are a few more pix showing the reinforcement, including steel straps over the vertices, plus two steel tension cables along the dome's "equator":

https://groups.google.com/forum/#!searchin/geodesichelp/Vermont$20dome/geodesichelp/XCG9qOAQmjU/D6RgqYPpx9oJ

The cupola was built on site last summer, then installed atop the dome via boom truck a few weeks ago. Pic attached.

- Gerry

On Saturday, September 6, 2014 1:39:02 PM UTC-4, Robert Clark wrote:

The more I look at the pictures of the 50 foot dome the more I am amazed.  It looks as though there is no connection at between the inner dome and the outer dome.  If so, the precision of the cutting and mitering is superb.  -Rob

[Gerry in Quebec]

Rob,

The project engineer made specific recommendations for various aspects of structural reinforcement, including the steel tension cables. However, nearly all the reinforcement measures were included, at least in general fashion, in the original design, based in part on the construction system used by Wil Fidroeff in Illinois, USA. He's the owner and brains behind the EconDome system (I think the company is called FazeChange Products). An architect also played an important role in the Vermont dome design, mainly for the interior layout of rooms and utilities.

Here's an earlier conversation about the Vermont dome:

https://groups.google.com/forum/#!searchin/geodesichelp/3$2F8%22$20steel/geodesichelp/Gg32ZLBCpAk/lTB3CSCEcegJ

- Gerry in Quebec

On Saturday, September 6, 2014 4:11:57 PM UTC-4, Robert Clark wrote:

I guess the strapping and metal cables are for hoop stress?  How did you calculate what would be needed?  Was the dome sized at all to make best use of OSB?  I love this project.  I can only dream of building something like that one day.  -Rob

[Gerry in Quebec]

Attached are a few photos of the 42' low-profile 5v icosa greenhouse in Washinton State, not far from Spokane.

- Gerry in Quebec

[Gerry in Quebec]

Hi Rob,

Try googling the Religious Center of Southern Illinois University. It's a 5v dome of this geometry, by Fuller & Sadao. Also, there's a discussion of flat-based domes in this Google group. You should find something by searching for the name "David Kruschke" or "Dave Kruschke".

- Gerry in wet & windy Quebec

On Wednesday, September 10, 2014 11:02:00 PM UTC-4, Robert Clark wrote:

Going in a different direction from trying to create a dome with as few different struts as possible, I thought I'd try to create a 5V dome with as many flat bases as possible.  What I came up with is a dome that except for the pent vertices, every other vertice lies on a potential flat base.  It gives a lot of choice.  -Rob

 

 

[Gerry in Quebec]

One more thing.... you'll also find a set of SketchUp models by Taff in the Trimble 3D warehouse. These are flat-based domes and mention the name Kruschke.

- Gerry

On Wednesday, September 10, 2014 11:02:00 PM UTC-4, Robert Clark wrote:

[Chris Kitrick]

This is an old thread but there is a 4 strut solution where all the vertices lie exactly on the surface of the sphere. I have attached a diagram with the angles / chord factors. There are 5 different faces.

Cheers,

Chris

[Hector Alfredo Hernández Hdez.]

I need to check this, there are 4 freedom liberty, and 5 constractions :)

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[Hector Alfredo Hernández Hdez.]

I know that one constractions is obataned freely

I will check a lot of solutions, i rememeber that exists a lot of.

[Adrian Rossiter]

Hi Chris

On Thu, 21 Mar 2019, Chris Kitrick wrote:
> This is an old thread but there is a 4 strut solution where all the
> vertices lie exactly on the surface of the sphere. I have attached a
> diagram with the angles / chord factors. There are 5 different faces.

I wondered about this, and so I wrote a program to solve this
kind of model. It confirmed your results

Result
------
Length ranges
0 : 0.1749151800138321 (+/-0.0000000000000007)
1 : 0.2048372210748026 (+/-0.0000000000000008)
2 : 0.2516217166432331 (+/-0.0000000000000015)
3 : 0.2458807628013209 (+/-0.0000000000000016)


I checked an octahedral version too, and this also worked out.

[Images attached]

[Hector Alfredo Hernández Hdez.]

Great

[Adrian Rossiter]

Hi Chris

On Thu, 21 Mar 2019, Chris Kitrick wrote:

> This is an old thread but there is a 4 strut solution where all the
> vertices lie exactly on the surface of the sphere. I have attached a
> diagram with the angles / chord factors. There are 5 different faces.

Are there just 4 differently shaped faces? With edges...

2 light blue, 1 dark blue
2 green, 1 dark blue
3 yellow
2 green, 1 yellow

[Chris Kitrick]

Adrian, you are correct. There are only 4 unique faces. Thus 4 edges and 4 faces.

Cheers,

Chris

[Ashok Mathur]

Chris 

Can you also provide the internal angles of these four triangles?

Thanks.

Regards

Ashok

--

[Chris Kitrick]

TRI        a               b               c               A               B               C

01   10.0347217337   11.7569238571   10.0347217337   54.4190035018   72.0000000000   54.4190035018

02   14.1236618257   11.7569238571   14.1236618257   65.8463007029   49.6340366331   65.8463007029

03   14.1236618257   14.1236618257   14.4551684518   59.7346957953   59.7346957953   62.0731926734

04   14.4551684518   14.4551684518   14.4551684518   60.5306084095   60.5306084095   60.5306084095

[Hector Alfredo Hernández Hdez.]

G

[Ashok Mathur]

Chris,

Thanks for the prompt reply.

One more question.

Is the dome flat at any truncation?

THANKS.

Regards

Ashok

[Chris Kitrick]

There are no perfectly flat truncations for this configuration.

Cheers

[Ashok Mathur]

Dear Chris

Thanks.

Regards

Ashok

[Hector Alfredo Hernández Hdez.]

Try this same desing, but using ocahedron, this will be sit flat to 5/10 fraction :)

El mié., 27 de mar. de 2019 a la(s) 18:50, Robert Clark (clark.rob...@gmail.com) escribió:

Chris, very elegant solution.  And, all vertices are equidistant from the center!

[Ashok Mathur]

At all frequency an octahedron has a flat base half way up.

Ashok

[Hector Alfredo Hernández Hdez.]

thats right,  but will the design be possible?

[Hector Alfredo Hernández Hdez.]

If we let  to some  r_i be different of 1, we will can add more constratios, such that sit flat for some  fraction dome.

All r_i =1 arent so important really

[Always Greener]

Hello,

 

could someone tell me what the numbers mean? {3,5+}5,0.

 

Is there a way to project this 5V onto the original icosahedron face? Or tell what happened to the Underlying icosahedron face to get this result? I am new to antiprism (this might be a foolish Question).

 

Can I get antiprism to Output this 5V and if yes then how?

 

Many Questions 😉

Thanks alot!

 

Greetings.

Florian

 

 

 

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[Chris Kitrick]

{m,n} is the geometry's Schläfli symbol 

m - represents the polygon (3=triangle,4=square,5=pentagon,etc.) 

n - represents the number of polygons around a vertex 

For geodesic tessellations based on the icosahedron the Schläfli symbol is {3,5+}

Each polygon is a triangle (m=3)

Each vertex has 5 or more polygons surrounding it (n=5+)

The full scope of geodesic tessellations includes the added (b,c) subscripts to the Schläfli symbol

{m,n}b,c

Typical geodesic forms:

Class I ( c is always 0 )

Class II ( b equals c )

Class III ( b not zero, c not zero, b not equal to c )

class III geometries are enantiomorphic or chiral (have handedness)

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[Always Greener]

I would like to get one 5V (with 4 struts) into Sketch-Up

In order to make it into a good karma dome like so:

 

https://www.youtube.com/watch?v=cLuu-zuDRJ8

 

, but I have no clue how. Someone has a game plan?

 

Let’s say I were to make a normal 5-V. How would I have to shift Vertices or lines to get to this.

I am really „colourblind“ here.

 

All operations have to happen on Guidelines with C-Points which would imply at least some partial flat Surface.

Usually this flat Surface is the Underlying icosahedron face.

 

I think the 5V is a good candidate for a dome. I also found this:

https://i.pinimg.com/originals/8d/46/34/8d4634279abc871d130b05463fd41ae8.jpg

Maybe this has a better Chance of making it into Sketchup?

 

Greetings!

 

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Von: Hector Alfredo Hernández Hdez.
Gesendet: Donnerstag, 28. März 2019 14:23
An: geodes...@googlegroups.com
Betreff: Re: 5V class-I dome requiring only 4 different struts

 

If we let  to some  r_i be different of 1, we will can add more constratios, such that sit flat for some  fraction dome.

[Adrian Rossiter]

Hi

On Thu, 18 Apr 2019, Always Greener wrote:
> I would like to get one 5V (with 4 struts) into Sketch-Up
> In order to make it into a good karma dome like so:
>
> https://www.youtube.com/watch?v=cLuu-zuDRJ8

Nice profile pic! [ http://www.antiprism.com/album/910_misc/gt08b_Med.jpg.5.html ]

> , but I have no clue how. Someone has a game plan?

I have attached a Collada version of the model. It should be possible
to import it into the paid-for version of Sketchup.

[Always Greener]

Thank you so much 😉.

 

 

I think this structure has great potential!

 

I hope you are ok with my profile Picture, I can Always Change it 😉.

V/r

Flo

 

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[Adrian Rossiter]

Hi

On Thu, 18 Apr 2019, Always Greener wrote:
> I hope you are ok with my profile Picture, I can Always Change it 😉.

It is fine to use it!

[Levente Likhanecz]

hi Always Greener,

attached sketchup file.

i used Chris figures to build.

the model is 1,000,000,000 radius to read directly all significant digits with tape measure tool (xxx+6 decimal). and approximate coloring.

i left aside the building "stones".

u can resize it to any dome radius suppose some proficiency with sketchup.

select the complete dome. then explode-explode-explode.... till u have everything exploded.

then make a single group of them.

then double click on it to open up the model.

choose tape measure tool.

click on dome center. then click on any vertex. it should then show 1,000,000,000.000000 and you have a guideline established.

type on your keyboard the requested radius - enter - say ok to resize.

finally u should have your radius dome.

cheers, lev

[Levente Likhanecz]

hi Adrian,

i have unpaid SU2017 and it imports collada without problem.

as with all other off2dae results no problemo.

cheers, lev

[Adrian Rossiter]

Hi Lev

On Fri, 19 Apr 2019, Levente Likhanecz wrote:
> i have unpaid SU2017 and it imports collada without problem.
> as with all other off2dae results no problemo.

Thanks for the info. I was trying with "SketchUp Free", which is
the web version. The only 3D format it will read is .skp.

Adrian

[Levente Likhanecz]

it is on my local pc and it is the free version of 2017. file menu -> import...

then there is a file type selector field with several selectable format including COLLADA(dae).

[Hector Alfredo Hernández Hdez.]

I like this desing so much !!

do you was who  calcutaled it?

On Thursday, March 21, 2019 at 2:31:48 PM UTC-7 Chris Kitrick wrote:

This is an old thread but there is a 4 strut solution where all the vertices lie exactly on the surface of the sphere. I have attached a diagram with the angles / chord factors. There are 5 different faces.

Cheers,

Chris

[Chris Kitrick]

Yes Hector, I created this optimization pattern with the 4 different struts. 

Cheers,

Chris

[Hector Alfredo Hernández Hdez.]

How do you do?

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