Geodesic Golden Ratio Egg

[Will]

Hey Taffgoch,

Ive been looking at your geodesic structures online, they look
fantastic!

Im working on a project that involves the creation of a geodesic egg
and I'd like the use the principles of Fibonnacci to create it. I
wondered if you would be able to explain how to create such an egg,
and if you could send an example of a golden ratio geodesic egg that
would be great too.

Cheers
Will

[TaffGoch]

Will,

Last month, I posted a SketchUp model of "The Seed" (Eden Project, UK) in the 3D Warehouse:

http://sketchup.google.com/3dwarehouse/details?mid=339d8ca5202250fdf4db8f25bbdf63f2

Is that what you're looking for?

______________________________

Making an 3D egg, in SketchUp, is not much different from drawing a sphere:

http://www.google.com/search?num=100&safe=on&q=sketchup+how+to+draw+an+egg

The golden ratio doesn't have to be the width-to-height-ratio of the egg, but you can certainly scale it so.

The fibonacci spiral isn't used in making the egg, either. Fibonacci spirals can be used to lay out the nodules, but, in fact, I didn't use them, at all, in making the Warehouse model.

I used the golden-angle to calculate, in an Excel spreadsheet, the x,y,z positions of the nodules, which I then imported into SketchUp. One "side-effect" is fibonacci spiral production. So, while I didn't employ the fibonacci sequence or spiral, it shows up in the final results, nevertheless.

The nodule-positioning method that I employed, in Excel, is that depicted in Figure 5, on page 10, of the following paper:

http://www.math.vanderbilt.edu/~esaff/texts/161.pdf

That's it -- those are all my secrets (all two of 'em,) regarding my making of "The Seed" model.

~Taff

[TaffGoch]

Will,

I found another development image that I had exported, while I was working-out the technique. It has only 1,600 guidepoint locations, while The Seed sculpture has 1,800 nodules.

~Taff

[TaffGoch]

BTW, the "phyllo" portion of the last image filename references "phyllotaxis," which can be studied, online.

http://images.google.com/search?as_q=phyllotaxis&hl=en&tbm=isch

[Will Bradley]

Hey Taffgoch,

Thanks for all the info! The main thing i am stuck with really is how to divide an egg up into the equilateral triangles. About a similar number of triangles to the one you created from a sphere then added a rounded point to it. I only know how to create a sphere that has squared faces... this probably seems really basic but thats what im stuck with!

Cheers Will

On Tue, Jul 5, 2011 at 7:11 PM, Will Bradley <willbr...@googlemail.com> wrote:

Hey Taffgoch,

Thanks for all the info! The main thing i am stuck with really is how to divide an egg up into the equilateral triangles. About a similar number of triangles to the one you created from a sphere then added a rounded point to it. I only know how to create a sphere that has squared faces... this probably seems really basic but thats what im stuck with!

Cheers Will

On Sun, Jun 19, 2011 at 10:13 PM, TaffGoch <taff...@gmail.com> wrote:

BTW, the "phyllo" portion of the last image filename references "phyllotaxis," which can be studied, online.

http://images.google.com/search?as_q=phyllotaxis&hl=en&tbm=isch

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[TaffGoch]

Hey, Will,

If you try to make a sphere (or egg) from equilateral triangles, you'll find it impossible. Equilateral triangles will ONLY produce a flat plane.

Even though geodesic domes appear to be composed of equilateral triangles, they aren't. The objective is, however, to make them as similar as possible, That's why I had to employ an Excel spreadsheet, to calculate the x,y,z coordinates for each point on the surface of the "egg." I would have to use a similar spreadsheet, to do the same for a sphere.

It is not "really basic," as it requires trigonometric algorithms to produce the 3D results. You are, indeed, "stuck," without the means to calculate the coordinates.

-Taff

[Blair Wolfram]

Equilateral triangles will ONLY produce a flat plane.

The icosahedron.

--

[TaffGoch]

I should amend my reply. Equilateral triangles can, indeed, produce 3D
volumes, but they aren't what you'd expect (or what you're after.)

See "Lobel frame"
http://sketchup.google.com/3dwarehouse/details?mid=d707c5785e8945e15267ed5eeb5c0a1c
(This is only one of several possible configurations.)

-Taff

[acmnewbie]

Dear Will,
Do visit the site of John Zerning to see Ellipsoidal Geodesic
structures ( Egg Shaped domes).

http://www.johnzerning.com/category/ellipsoid/

In fact the entire site is worth a good look.
Regards
Ashok

On Jul 5, 11:28 pm, Will Bradley <willbradl...@googlemail.com> wrote:
> Hey Taffgoch,
>
> Thanks for all the info! The main thing i am stuck with really is how to
> divide an egg up into the equilateral triangles. About a similar number of
> triangles to the one you created from a sphere then added a rounded point to
> it. I only know how to create a sphere that has squared faces... this
> probably seems really basic but thats what im stuck with!
>
> Cheers Will
>

> On Tue, Jul 5, 2011 at 7:11 PM, Will Bradley <willbradl...@googlemail.com>wrote:
>
>
>
>
>
>
>
> > Hey Taffgoch,
>
> > Thanks for all the info! The main thing i am stuck with really is how to
> > divide an egg up into the equilateral triangles. About a similar number of
> > triangles to the one you created from a sphere then added a rounded point to
> > it. I only know how to create a sphere that has squared faces... this
> > probably seems really basic but thats what im stuck with!
>
> > Cheers Will
>

[Gerry in Quebec]

Don't forget the icosahedron's little siblings, the tetrahedron and
octahedron.

> > For more options, visithttp://groups.google.com/group/geodesichelp?hl=en- Hide quoted text -
>
> - Show quoted text -

[Camilla Fox]

You can potentially take the points, and crank them through a convex
hull triangulator like qhull (hint: to get triangles rather than
tetrahedrons, add a bunch of bogus interior and exterior points, then
prune from your list of tetrahedrons any faces that touch one of the
bogus points - what's left is your triangles).

I think the phyllotaxis layouts only really work with large numbers of
points, and construction will be constrained by every piece being
unique. Visually, it's a layout that takes well to curves, and not to
straight lines. For smaller projects, you may want to consider an
iterative algorithm where you adjust the points based on the
properties you want in the triangulation.

-Camilla

[Paul Kranz]

Taff:

 

Aren't the tetrahedron, octahedron and icosahedron geodesic spheres "composed of equilateral triangles?"

 

Paul sends...

--

[TaffGoch]

Truly, Paul,

A couple of other posts have been made, pointing out my oversight.

(At the time, I was thinking of subdividing, with many triangles, the surface of a sphere.)

Of course, I do, indeed, know that most of the Platonic solids have equilateral triangle faces.

Chagrined,

Taff

[Paul Kranz]

Forgiven!

Taff

--

[hahajahah]

Hi there 

It may help you cos I was wondering about geodesic egg from about half year, 

http://sketchup.google.com/3dwarehouse/details?mid=a5b1154eaceef4aafbc0065e271be45f&ct=mdsa&prevstart=0

The more frecuency the egg looks finer, this one is 12v . i used gnomic projection for that as the Walther Bauersfeld in 1926.

this egg proprtions width to height fit in to golden ratio.

[Ken G. Brown]

Here's a full size one in Vegreville, AB, by the late Ronald Resch. 
<http://www.google.ca/search?hl=en&client=safari&q=vegreville+egg&oq=vegreville+egg&aq=0&aqi=g3g-v2&aql=1&gs_sm=c&gs_upl=8971l15128l0l17359l18l13l1l0l0l2l557l2323l0.1.1.4.0.1l7l0&mvs=0>

Ken,

from my iPhone

--

[hahajahah]

Hie there

That`s realy nice egg , do you know actual dimensions and how or what
was used to make this construction.
My aim for them geodesic structures is to make them in real time and
space,so i just need to know exact dimensions of struts and conctors,
also im fixing my drawings so they mach exact measurments and match
the symetry of a trinagle consist in it. The problem with my egg is
that have difrent ends, one is bigger and can be a half sphere but
other one radiusis almost threee times smaller and theres a problem
becouse al the triangles are difrent and map for construction is very
difrent and can be wast like in 36 v geodesic egg wich aim working on
now.

peace and love

On Sep 26, 7:39 am, "Ken G. Brown" <kbr...@mac.com> wrote:
> Here's a full size one in Vegreville, AB, by the late Ronald Resch.

> <http://www.google.ca/search?hl=en&client=safari&q=vegreville+egg&oq=v...>

>
> Ken,
> from my iPhone
>
> On 2011-09-25, at 11:32, hahajahah <los...@gmail.com> wrote:
>
>
>
>
>
>
>
> > Hi there
>
> > It may help you cos I was wondering about geodesic egg from about half year,

> >http://sketchup.google.com/3dwarehouse/details?mid=a5b1154eaceef4aafb...

[hahajahah]

Hi 

After discussion about roskilde dome and this manner of making geodesic net

i decided to make model similar to that construction with my egg here are results attached.

After we obtain shape that will be better to work with, in real life its possible to make 

lots of good things like ..... whatever imagine.

Most important is that it would be impossible without help and fruity talks on this particular group 

thanx to all guys ....

Peace and respect

[TaffGoch]

Looks like more readers are getting-out the paper and scissors.

Using "fat" struts makes the Roskilde domes work, and helps here, too.
Without the "beefiness" of the wide struts, hexagons & pentagons would
stretch and sag, from gravity's forces on the model.

Insightful implementation of the concept....

-Taff

[TaffGoch]

Here's another post that didn't make it through to the group discussion list. (That's two this week.)

__________________________________

Fri, Jan 11, 2013, hahajahah wrote:

Hi

Yes I was amaze what strength this net can produce in this more sophisticated model.

This one is 65 cm high and is no way that will bend inward, when  i only use technical cardboard.

I hope next one will not fit inside my house ;)

[Ashok Mathur]

Dear All,

I am not starting a new topic but am adding to an old discussion.

The latest posting in Masonary Design Blog has interesting write up on Fibonacci  numbers and icosahedrons.
.
Old stuff to those who have been following this topic, but with vivid photos

http://masonrydesign.blogspot.in/2014/06/fibonacci-masonry.html?utm_source=feedburner&utm_medium=email&utm_campaign=Feed:+MasonryDesign+%28Masonry+Design%29

Regards
Ashok

[Blair Wolfram]

Great page Ashok!

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thedo...@domeincorporated.com

http://www.hurricanedomes.com

888-DOME-INC or 612-333-3663

[Rishabh Arora]

I am building a truncated ellipsoid, for the interiors of a company. I need to model and replicate it at site. It needs to be made with a wooden frame preferably without hubs. Any ideas? I am completely lost! Please help!

[Ashok Mathur]

Dear Rishab

The term 'truncated ellipsoid' does not convey as much as truncated sphere does.

For others to understand what you want to build, you need to provide additional details such as given below.

A truncated ellipsoid could have a circular plan floor or the floor plan could also be elliptical.

If you are looking at an elliptical floor plan as well as an elliptical upper structure, then be aware that the two need not have the same elliptical ratios.

John Rich of New Zealand has done wonderful work in this regard.

Also there are very good Octahedron based solutions mentioned in this forums.

If a circular floor plan is acceptable to you  and what you want is that the radius of the floor plan is much larger than its height, then what you are looking at is called by me as an shallow cap Icosahedron.

Gerry has posted full solutions for this Golden ratio  structure.

Regards

Ashok

Regards

Ashok

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[Ashok Mathur]

Dear Rishab

Hugh Kenner in his book Geodesic Maths and How to use it has given full details on calculating elliptical structures with elliptical floor plans.

Its computationally heavy but not difficult.

Regards

Ashok

Regards

Ashok

[TaffGoch]

Rishabh,

The SketchUp plugin that I use, to obtain an ovoid shape, is called "FredoScale"
http://sketchucation.com/forums/viewtopic.php?f=180&t=17948

An ellipsoid requires no special plugin, as such can be achieved with native SketchUp scaling tools.

-Taff

[Paul Kranz]

Taff: Do you have a fav online . Sketch
Up tutorial? Paul sends...

--

[TaffGoch]

Paul,

For learning SketchUp, step-by-step?

Well, there used to be a pretty good set of tutorials, produced by the SketchUp developers, but that has vanished. They decided to substitute YouTube videos, and established a channel for tutorials and demos:  https://www.youtube.com/user/SketchUpVideo/videos  (I have to admit, they're pretty good.)

If you search YouTube, you'll find that hundreds of other authors now publish tutorials, as well. Some authors started out with regular, paced tutorial podcasts.
https://www.youtube.com/results?search_query=sketchup

By default, YouTube has become the place to go for SketchUp tutorials.
_______________________________

I always make sure that a student of mine learns, early-on, how to rotate geometry around ANY axis:
https://sites.google.com/site/sketchupsage/tweak/rotate#TOC-Folding-along-an-axis-of-rotation-

BTW, the SketchUp Sage website is a great learning resource.

-Taff

[Paul Kranz]

Taff: Great info, thank you very much! Paul sends...

--

[Rishabh Arora]

Hi Ashok, 

Thank you for your response, I will attach an image to explain what I am trying to build. I truncated and scaled the golden egg shared by Taff as per my requirements. How do I build this accurately? I know the width, height and depth that I need.
​

On Tue, Sep 6, 2016 at 9:29 PM, Ashok Mathur <ashokch...@gmail.com> wrote:

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[Ashok Mathur]

Dear Rishab

The shape and its truncation that you have chosen does not seem to have any axis of symmetry.

If there are no axis of symmetry, then the chords for every pair of adjacent points have to be calculated as per Hugh Kenner' s method. Look up Chapter 13 pages 84 to 94 of the book. (https://www.scribd.com/doc/61829724/1976-Hugh-Kenner-Geodesic-Math-and-How-to-Use-It)

I am not aware if the anybody has made a computer programme for doing this work.

If you do make one, please share it with all.

Regards

Ashok

Regards

Ashok

[Rishabh Arora]

Hi Ashok

The structure is symmetrical along the longer side. Imagine it as an ovoid/egg truncated horizontally below its central horizontal plane. I did it to retain proportion of the structure, as the height I need it fixed at 2600mm.

[Ashok Mathur]

Dear Rishab

If it symmetrical about the long axis , your work has been halved.

But do ask Taff if there are other symmetries that you might have missed.

Regards

Ashok

Regards

Ashok

[Rishabh Arora]

The question remain. How do I calculate and execute the structure?

[Ashok Mathur]

Q. How do I calculate the structure?

Ans : 1.The co-ordinates of half the vertices have to be computed. It can be done in terms of Cartesian co-ordinates or spherical co-ordinates. Spherical co-ordinates are the method of choice if you already know them.

2. Distance between two adjacent co-ordinates have to be computed. The formulas for such computation are given between pages 84 to 94 of Chapter 13 of Hugh Kenner's book. The distances are the chord factors.

3.Dihedral angles between different pairs of faces need to be computed.

Q How do I execute the structure?

1 Choose the material you are going to work with :MS steel struts; Aluminium tubing, Plywood, 2by 4 timber etc.

2. Choose the appropriate hub that will go well with your strut choice.

3. Cut the struts and label them properly and carefully as you will have a huge number of similar but different struts.

4. Chose what method of assembly you like. The alternatives are : start with the highest vertex being assembled first and then pushed upwards or start with the bottom of the structure being assembled first and the highest vertex being assembled last.

5. Do you need a crane/central mast to help you with assembly or steep ladders will do?

Execute the plan.

If you want a set of photographs that illustrate this, I can give you links.

Regards

Ashok

Regards

Ashok

[Rishabh Arora]

Thank you so much for the detailed explanation! I don't know how to compute these elements so, I will go through it and try to understand.

[TaffGoch]

Rishabh,

I assume that you used SketchUp to position the egg and scale it to the size required.  So, why are you not using SketchUp to read 'Entity Info' for lengths?

SketchUp can also report cartesian coordinates of endpoints, using the 'Text' tool, to label, when "pointing to" a vertex:

SketchUp may be more versatile than you've been led to believe. Personally, I find that it's fully-capable of providing all the tools and resources that I need for such projects (lengths, angles, coordinates, scaling, etc.)
______________________

Regarding design, I am wondering whether you need the complexity of a 9-frequency dome. Most moderate-scale domes are 3-to-6 frequency. It would, certainly, save you a lot of work, if you would establish the longest strut (or largest panel) that you think you will be using, then use that measurement to determine the lowest-possible frequency to achieve your objective dome. (In other words, let material availability determine the frequency.)

-Taff

[Sacred Life Seeds]

This is so so so amazing ~ how has this developed ?

[Sacred Life Seeds]

could something like this be done for pent geometry

~ross

On Friday, January 11, 2013 at 1:01:47 PM UTC-7, TaffGoch wrote: