Hexdome calculator

[Travelling Telescope]

Hi all,

Does anyone know where I can find a calculator for the duals of a geodesic dome?  Attached image is close to what I'm looking for..

Thanks in advance!

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[Gerry in Quebec]

Hi Daniel,

Looks like an interesting science awareness project. Unfortunately, I could't open the image file you posted.

- Gerry in Québec

[TaffGoch]

Gerry, (and all)

Add a ".jpg" extension to the filename:

(hexdome.jpg)

-Taff

(aka, TaffGoch, David Price)

[Gerry in Quebec]

Hi Daniel (& Taff),

The polyhedral software "Antiprism" should be able to generate the dual of a geodesic dome.

 In looking at your jpg (reposted by Taff.... thanks), I see that the hex-pent structure you're interested in is probably a design by. Robert Clark, a member of this group. Maybe he can help you with that.

Here on Geodesic Help, we also had a discussion in Feb. 2016 about a greenhouse design with a very similar layout. It sits flat at the equator. Here's a link to the discussion back in Feb. 2016, which includes a file showing panel dimensions.

https://groups.google.com/forum/#!searchin/geodesichelp/B$20$3D$200.1964544;context-place=forum/geodesichelp

I'm also including an image showing four items: the 4v, class II structure, the hex-pent dual of that structure, the two together WITHOUT connecting struts, and the two together, WITH connecting struts to form a space frame similar to the Montreal Biosphere built by Fuller & Sadao in the 1960s.

 

- Gerry in Québec

[RC]

Daniel,

I'm not quite sure what you're looking for, but I stayed a little late after work today to remodel the picture of the dome you posted.  It is a 10 meter diameter hemisphere and sits flat on the ground.  Dimensions are in inches.  Struts would be laminated from strips of plywood glued and screwed together to create arched pieces of wood. There are 3 hub types and 3 strut lengths. Each of the hubs has bi-lateral symmetry.

Robert

On Tuesday, November 1, 2022 at 8:10:04 AM UTC-4 daniel...@gmail.com wrote:

[Travelling Telescope]

Hi Robert,Gerry & Taff,

Thank you all so, so much for all this information - it's so great to have your help with this!!  RC - not sure I totally understand your design - I think the numbers seems to be in degrees of a circle for the curves of the struts, but I can't see (or don't understand!) where the strut lengths are! 

I love this design tho - I'd really like to try it with bamboo - and bend the struts exactly as your calculations show, to create a really round structure.

Thanks again!

Chu

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[RC]

Daniel,

The lengths of the struts for the 30 meter dome were:

35.223"

37.043"

40.475"

Yesterday, I was anxious to get out of the office and go home so I just through up a bunch of loose pictures and information.  I haven't even pointed out which of the 3 hubs are which, and which of the 3 struts are which.  If you're still interested in this type of dome then I'll mark it up.

[Travelling Telescope]

Hi RC - I am definitely interested in this dome!!  Would love to know more whenever you have time - no rush!  And earlier you mentioned the dome was 10m, but in your most recent email it says 30m which I presume was meant to be feet (?).  Thanks again

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[RC]

Yeah, I meant 10 meters.  It was the end of the day and I was rushing.  Is this the planetarium dome with the suspended cloth screen?

[Travelling Telescope]

It is, but my intention is to try a new screen of woven hexagonal & pentagonal segments..

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[RC]

Why the woven screen as opposed to a sewn cloth screen?  Cloth seems like it would be easier to fabricate and would project clearer star images.  I would think that almost every rural indiginous village would have access to some cheap cloth.

[Travelling Telescope]

I'd love to do this but I can't figure out how to get fabric not to sag...

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[RC]

What if the screen were made from a light fabric with slight amount of stretch to it?  It could be sewn from pentagons and hexgons matching the shapes of those of the dome, but a little smaller in scale (95%).  The fabric screen could then be attached by string at each vertice of the screen dome to each corresponding vertice of the supporting hex dome frame.  When each string is tensioned and tied off, the fabric screen should become taught and wrinkle free.

[Dx G]

Hi folks,

 Nice work on the hexdome.  A few thoughts about the tension for the cover.

1) If one took some narrow strips of something like shrink wrap, packaging tape, or other suitable material, straps could run from the center of one strut to the center of the strut on the opposite side. This would give the cover fabric some support and might prevent sagging.  Baler twine is also a real good material for trying things out, its inexpensive, very weatherproof and comes in a wide selection of sizes and tensile strength.

2) If you have never considered the use of a triaxial weave, take a look at it and at least be aware of this as a possible option. In particular,, especially when you consider that, unlike rectilinear structures, domes have a lot of triangular logistics and are more compatible with this form of fabric(s).

triaxial weaving
https://www.youtube.com/watch?v=KEwKtsGnnlc

https://hexdome.com/weaving/triaxial/index.php

https://www.antiprism.com/album/830_woven_polys/index.html

(thanks adrian)

DxG

[RC]

Here is the color coded layout and dimensions for struts with hole locations (in inches)

[Dick Fischbeck]

Nice documentation. Anyone can follow it.

Did Fuller or others make a similar structure? I'm guessing yes, but I don't recall.

[got2f...@yahoo.com]

Maybe you could incorporate batten pockets that are sewn or glued onto the fabric panels and slip in curved battens with the needed dome radius much like one does setting up a hang glider to form the curved upper surface. They could be a tad too long and be forced to curve or they are stiff and stay bowed...I'm sort of working on a similar project, a ceiling dome to cover up Icynene that is raining dust....it has to be soft (not flammable )to tame the acoustics since it is a big open room  without  partitions...
 

On Thursday, November 3, 2022 at 4:13:58 PM UTC-4 daniel...@gmail.com wrote:

[Remco]

Hi There

I am hoping someone would have a basic model of a polyhedra or sphere with either 48 or 50 faces ( or the next nearest amount ) ?

     This would be greatly appreciated  ( SketchUp preferable ? )

        Many Thanks Remco 

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[Gerry in Quebec]

Hi Remco,

This polyhedron has 48 faces:

https://en.wikipedia.org/wiki/Disdyakis_dodecahedron

I have a model of a similar geodesic sphere which I should be able to convert to a SketchUp compatible format. I'll hold off doing so for a bit in case someone else in the group has a more suitable polyhedron model to show you.

- Gerry in Québec

[Ashok Mathur]

Dear Remco

Start with a simple Icosahedron

Faces = 20 triangles

Edges = 30

Vertex =.12

General equation F= E - V + 2

As a two way subdivision yields 80 faces, neither the icosahedron or its first subdivision will come any where your requirements.

Let’s us look at one more triangle based structure, Octahedron

Faces = 8 triangles

Edges = 12 

Vertex = 6

The first subdivision yields 32 triangles so this may be a good subdivision to begin with.

Some triangles are further subdivided while others are joined to form a rhombus till you 

the range of faces you have set for yourself.

Tetra will not yield worth while results as number of triangles jump from 16 to 64.

Is this the type of thinking you are looking for or you want a final answer?

Regards

Ashok

Sent from my iPhone

On 26-Apr-2023, at 8:02 AM, Gerry in Quebec <toomey...@gmail.com> wrote:

Hi Remco,

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[Ashok Mathur]

Ready made answer

In geometry, the snub cube, or snub cuboctahedron, is an Archimedean solid with 38 faces: 6 squares and 32 equilateral triangles. It has 60 edges and 24 vertices. It is a chiral polyhedron; that is, it has two distinct forms, which are mirror images of each other. Wikipedia

Sent from my iPhone

On 26-Apr-2023, at 6:38 AM, Remco <re...@remcodefouw.net> wrote:

Hi There

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[Adrian Rossiter]

Hi Remco

On Mon, 24 Apr 2023, Remco wrote:
> I am hoping someone would have a basic model of a polyhedra or sphere with either 48 or 50 faces ( or the next nearest amount ) ?
>
> This would be greatly appreciated ( SketchUp preferable ? )

I'm not too sure of your requirements, but as the thread seems to refer
to "hexpents", you could spread some points on a sphere, find the convex
hull, make a dual, them find the canonical form (for a more even result).
E.g. 49 faces [image attached]

repel -N 49 | conv_hull | pol_recip | canonical | antiview

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

[Erich Nolan Bertussi]

awesome discussion thread!

merci beaucoup ami!

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[Remco]

Hi Gerry in Québec

  Thats fantastic , thank you very much indeed 

 This is a Screen shot of the thing im working on, one of 5 x  2meter diameter 8 meter high Sculptures with working prisms

Fo the national Childerns hospital Dublin Ireland 

     Regards and thanks  Remco 

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[Gerry Toomey]

Hi Remco,
Here are bare-bones SketchUp files of two polyhedra, each with 48 faces.
All the vertices lie on the circumsphere and the spherical radius of each model is 1 unit.

Good luck with the sculptures & please post some pix once the project is completed.
Cheers,
- Gerry in Québec

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[Ashok Mathur]

Dear Gerry

How many different strut lengths are there in the polyhedra?

I count upto 4 but may be there are five?

How many unique triangles ?

Regards

Ashok

Sent from my iPhone

On 30-Apr-2023, at 12:02 PM, Gerry Toomey <toomey...@gmail.com> wrote:



Hi Remco,
Here are bare-bones SketchUp files of two polyhedra, each with 48 faces.
All the vertices lie on the circumsphere and the spherical radius of each model is 1 unit.

Good luck with the sculptures & please post some pix once the project is completed.
Cheers,
- Gerry in Québec

<Polyhedron-48-faces-Remco-1.png>

<Polyhedron-48-faces-Remco-2.png>

Virus-free.www.avast.com

On Sat, Apr 29, 2023 at 8:30 PM Remco <re...@remcodefouw.net> wrote:

Hi Gerry in Québec

  Thats fantastic , thank you very much indeed 

 This is a Screen shot of the thing im working on, one of 5 x  2meter diameter 8 meter high Sculptures with working prisms

Fo the national Childerns hospital Dublin Ireland 

     Regards and thanks  Remco 

<Screenshot 2023-04-26 at 08.16.48.png>

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<Geosphere-48-faces-Remco-2.skp>

<Geosphere-48-faces-Remco-1.skp>

[Gerry in Quebec]

Hi Ashok,
In the Remco-1.model, there are 4 edge lengths and 4 types of triangular faces, one being the mirror image of another.
In the Remco-2 model there are 3 edge lengths and 2 face types, again one being the mirror image of the other.

- Gerry in Québec

[Ashok Mathur]

Dear Gerry,

Please help me and correct me as I am not sure of my counting.

I have exploded your second image into parts as shown below.

Original Image	Two identical caps	The remaining barrel	Eight faces of the barrel
	8 faces per cap 16 faces in caps.		6 faces per barrel face eight in number.  48 faces in the barrel.

So I find a total of 64 faces.

The earlier figure has 48 faces but looks very weak along the straight edges that connect the two caps.

Regards

Ashok

Regards

Ashok

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[Dick Fischbeck]

So, by using all 4 and 6 way vertexes, you don't need any 5 ways?

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[Dick Fischbeck]

I guess it is octa and not icosa.

[Gerry in Quebec]

Hi Ashok & Dick,

Ashok, each cap has 6 triangles, not 8. I've included an overhead view of one of the caps. Total faces = 48.

As for the other polyhedron, the one that resembles a disdyakis dodecahedron, the dihedral angle between some pairs of faces in the caps is quite large, namely 173.07 degrees. So, you're right, if it were being used as a building, there might be a structural problem. But the choice of that polyhedron was simply to give Remco an option to consider, for projecting the spikes of his floral sculpture.

Dick, yes,  there are only 4-way and 6-way vertices. The starting point for modeling that polyhedron was neither the octahedron nor the icosahedron, rather a hexagonal pyramid (where height = base radius). I applied a 2v breakdown, making all vertices equidistant from the centre of the pyramid floor. Then I added a second identical 2v hex pyramid,  aligning them floor to floor. Presto, a 48-faced polyhedron.

Cheers,

- Gerry in Québec

[Dick Fischbeck]

Let me add, Jerry, I usually think in terms of structures for practical reasons.  The tet, the  octa and the icosa. 

Thanks!

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[Dick Fischbeck]

Sorry. Gerry. We are in the same neighborhood after all!