Geodesic Dome Origami - Believe It!

[TaffGoch]

Holy Smoke!

Here is a Class-I, 4-frequency geodesic dome, folded from a flat sheet of material:

[TaffGoch]

Here's the source: http://www.flickr.com/photos/tactom/6850190198/

And here's the crease pattern:

[TaffGoch]

You can find a crease pattern, twice as big, at: http://www.flickr.com/photos/tactom/7007998219

[homespun]

Oh, Taff, why dost thou tempt me yet again?

                                     Dan

[TaffGoch]

I was wondering if such a thing was possible. I'm happy to say that I didn't have to develop it myself. Personally, I would have started with 2v and 3v frequencies.

Here's the triangle "origami tessellation" concept, with simpler crease pattern (on the far-right, in the last image):

[homespun]

Taff, 

I checked out his Flickr and found this one - attached.

Any ideas how I could duplicate it in "papercarft"?

Let me know when you get tired of making these patterns for me - I'm insatiable.

                             Dan

----- Original Message -----

From: TaffGoch

To: Geodesic Help Group

Sent: Friday, January 11, 2013 3:10 PM

Subject: Re: Geodesic Dome Origami - Believe It!

[TaffGoch]

Dan,

Found the originating art page, and a bit-larger image to study: http://www.flickr.com/photos/carlosnmolina/6998394393/

No tabs (yet,) but I figured you, too, would just as well be able to add them.

-Taff

[Ken G. Brown]

Have a look at patents by Ronald D Resch

<http://www.google.com/search?hl=en&tbo=d&tbm=pts&q=ronald+d+resch+&oq=ronald+d+resch+&gs_l=mobile-gws-serp.12..0i7i30j0i30.127323.137969.0.146616.17.12.0.0.0.0.301.1883.0j10j1j1.12.0...0.0...1ac.1.bCc5fECCSrg>

He developed systems of construction by studying natural folding patterns resulting from randomly scrunching up paper. 

Ken,

from my iPhone

On 2013-01-11, at 14:59, TaffGoch <taff...@gmail.com> wrote:

I was wondering if such a thing was possible. I'm happy to say that I didn't have to develop it myself. Personally, I would have started with 2v and 3v frequencies.

Here's the triangle "origami tessellation" concept, with simpler crease pattern (on the far-right, in the last image):

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<294547104_5da0e673dd_o.png>

<ron-resch_02.jpeg>

<3343503879_2a48638d4d_b.jpg>

[homespun]

Taff,

   Thanks.  Yes, I can do the tabs....

             Dan

----- Original Message -----

From: TaffGoch

To: geodes...@googlegroups.com

Sent: Friday, January 11, 2013 10:09 PM

Subject: Re: Geodesic Dome Origami - Believe It!

--

[homespun]

Here it is!.  I made it with holes for reaching in.

[TaffGoch]

I was wondering how you were going to glue the final tabs.

I thought about saving pertinent pentagons unglued, until last.

[homespun]

 

Taff --

       How about this one?  -- another by Carlos Molina...

       I am trying to contact him - so far no reply.

                         Dan 

----- Original Message -----

From: TaffGoch

To: geodes...@googlegroups.com

Sent: Saturday, January 12, 2013 7:23 PM

Subject: Re: Geodesic Dome Origami - Believe It!

I was wondering how you were going to glue the final tabs.

I thought about saving pertinent pentagons unglued, until last.

-- 

[TaffGoch]

Dan,

It's hard to tell what's going on, deep inside those cavities (where the curves intersect.)

To start, I experimented with something a little simpler -- an icosahedron:

[homespun]

Taff,

   Thanks!  I figured it was an icosahedron.  So I could try making 30 of the pattern you sent (with tabs, of course), or, better yet, I could do 60, each with a "triangle" and a "petal" and glue two petals on top each other, much in the way that the pentagons were gluded on top of each other in the previous model.  That would give me a way to reach in and pinch tabs together, like you had suggested instead of making holes.  What do you think?

             Dan

----- Original Message -----

From: TaffGoch

To: geodes...@googlegroups.com

Sent: Monday, January 14, 2013 3:18 PM

Subject: Re: Geodesic Dome Origami - Believe It!

[TaffGoch]

Overlapping petals (2/3 of a pattern) should work nicely.

I'm experimenting with modeling the 2v version, as depicted in your previously-attached image....

[homespun]

I'm looking at both together --- Is the one I sent really like a dimpled dodecahedron, with each penatagonal face resolved into triangles, and then "spericalized" with petals and curved folds?

----- Original Message -----

From: TaffGoch

To: geodes...@googlegroups.com

Sent: Monday, January 14, 2013 4:59 PM

Subject: Re: Geodesic Dome Origami - Believe It!

[TaffGoch]

I appears to be based on a Class-II, 2-frequency tessellation of the icosahedron:

[TaffGoch]

This looks about right. I haven't, yet, developed the pattern....

[homespun]

Taff,

    Looks so pretty.

    I have already started working on the little one, the icosahedron.  Just need to make 20 sections and glue them petal upon petal.  Should be easy....

                        Dan

----- Original Message -----

From: TaffGoch

To: geodes...@googlegroups.com

Sent: Monday, January 14, 2013 6:20 PM

Subject: Re: Geodesic Dome Origami - Believe It!

[TaffGoch]

For this model, there are two different patterns.

The pattern for the modules (60) that form the pent stars differs from the pattern for the modules (30) that form the pent edges.

Also, note that the pent-star modules are asymmetrical (up/down,) while the pent-edge modules are symmetrical. In the asymmetrical pent-star, the uppermost vertex of the pattern (as depicted below) points to the center of the pent "star."

Be careful when folding & assembling, keeping them in separate "piles." Before cutting them out, you may want to make a mark, on the backside of the asymmetrical pent-star pattern, indicating the center-pointing vertex.

I hope that all makes sense....

[TaffGoch]

Oh, also, when printing the patterns, make sure to use the same scaling factor (percentage) for the different patterns.

That goes without saying, perhaps, but it's an easy mistake to make, with the way printer settings are typically configured....

[Paul Robinson]

I would call this a pentakis dodecahedron, as the pentagons sit back to back on an icosahedron they face each other point to point... Or am I wrong?

I find some of the mathematical terms in geodesic dome geometry very confusing, must sound like double dutch to the uninitiated.

Oh as we are maybe talking about the pentakis dodecahedron, is it the only polyhedra with 60 face all the same shape and dihedral angles that are  equal or are there others?

On 14 Jan 2013, at 23:16, TaffGoch wrote:

I appears to be based on a Class-II, 2-frequency tessellation of the icosahedron:

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<Lens 2v.png>

[homespun]

Taff,

   Thanks so much.  I believe I understand about the two different patterns.

 

   First I will finish the little one, the icosahedron.  I have found that after the glue dries, it's best to trim down the tabs as much as possible as otherwise they tend to get in each others way as the model progresses.  I have completed the first pentagonal flower section.

 

   Just think, a couple of weeks ago I didn't even know there was sush a thing as a "curved fold", and now I am going crazy with them.....

   I have been quite prolific with these models in the last few weeks, as the college has been between sections, but I go back to work in another week.

 

   Dan

----- Original Message -----

From: TaffGoch

To: geodes...@googlegroups.com

Sent: Monday, January 14, 2013 8:05 PM

Subject: Re: Geodesic Dome Origami - Believe It!

[TaffGoch]

Paul,

It is, indeed, called a pentakis dodecahedron. (I've read descriptions of the EPCOT Spaceship Earth being based on the pentakis dodecahedron.)

It is, also, a class-II, frequency 2v tessellation. It just depends on what reference you happen to be reading. Both descriptions are correct.

-Taff

[Adrian Rossiter]

Hi Paul

On Tue, 15 Jan 2013, Paul Robinson wrote:
> Oh as we are maybe talking about the pentakis dodecahedron, is it the only
> polyhedra with 60 face all the same shape and dihedral angles that are equal
> or are there others?

In the "kis" family there is also a triakis icosahedron and a
dipyramid based on a 30-sided polygon, which can be constructed
to have all equal dihedral angles.

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

[homespun]

First Model Completed - will start 2nd this evening....
Dan

[Gerry Toomey]

As Paul Robinson mentioned, the pentakisdodecahedron has the same dihedal angle over all edges (156.719 degrees). Its dual is the buckyball, or truncated icosahedron. While the class II, 2v icosa geodesic sphere looks quite similar to the pentakisdodecahedron, it has two dihedral angles: 161.946 over the long edges and 153.790 over the short edges. Another lookalike is the rhombic triacontahedron which has diamond-shaped faces.The dihedral over its edges is 144 degrees. The attached jpg compares the various radii of these three polyhedral cousins. With such family resemblance, it's easy to see why several different terms are used to designate class II hex-pent structures, which of course can be a bit confusing.

 

- Gerry in Quebec

[TaffGoch]

Ah, so,

The vertex-to-center radii are not both equal to 1.0, which is the case for the geodesic tessellation.

[homespun]

Taff,

   I have completed 2 pentagonal sections of the "Flower" 2V Geodesic Sphere model.  Attached picture shows the model inside-out.  The tips of the "dimples" touch and interfere with each other so that I will not be able to attach a 3rd section.  Either the valleys are too deep, or the I will have to truncate them.  HELP!

[TaffGoch]

Dan,

I was thinking, last night, of how I could simplify the model, to make assembly easier. I came up with this, while drifting off to sleep.

The pattern will make a triangular module, depicted in the second image. Each "petal" will completely overlap an adjacent-module petal. You'll need 60 modules. This should make assembly much less-complicated. (I'm fairly confident that the pattern will produce the correct angles for smooth overlap.)

I color-coded this one, to make correct module adjacency/orientation more-obvious.

(Recommend abandoning the previous version.)

[homespun]

Taff,

   I was making similar triangular models in my own way, using "pent-star" left, "pent-star" right, and "pent-edge" to make them.

   I have some concerns about the new pattern:

           1)  Shouldn't the folds in the depressions be curved folds to be more like the original model picture?

           2)  Are the depressions in the modules now shallow enough so that they won't interfere?

 

  I have been working on my own to modify your original patterns to make the derpressions more shallow.

                        Dan

----- Original Message -----

From: TaffGoch

To: geodes...@googlegroups.com

Sent: Wednesday, January 16, 2013 5:38 PM

Subject: Re: Geodesic Dome Origami - Believe It!

[TaffGoch]

The "depressions" are more-shallow -- but, not by a lot.

The main change is a switch from cylindrical side walls, to conical side walls. This permits the straight-line shared edges in the pattern. If the cylindrical side walls had been retained, the adjacent edges would, indeed, remain curved, which would not have allowed the simpler pattern. Overall, the completed model looks identical. It's a subtle change.

I'm hoping that you'll find that this pattern works better (even though I haven't physically tried it, myself.) I'll print-out a pattern, and see how a module looks, compared to the computer model.

-Taff

[homespun]

Taff,

   Silly me.  I realized finally that I had closed up the florets improperly so that from the outside they were concave rather than convex.  And that why the depressions were bumping into each other.  So the original pattern would have worked fine if I hadn't messed up.  Anyway, not realizing that, I went ahead and modified the pattern so the depressions were not as deep, and things are proceeding well.  I decided not to use the new pattern you offered because I am growing rather fond of curved folds and wanted to stick with them, rather than opt out fot the straight folds.  Will send a picture tomorrow after I finish three sections.

              Dan

----- Original Message -----

From: TaffGoch

To: geodes...@googlegroups.com

Sent: Wednesday, January 16, 2013 5:38 PM

Subject: Re: Geodesic Dome Origami - Believe It!

[homespun]

Taff,

   OK.  Here it is with three sections assembled.  As I said, I used a modified version of your original pattern, adjusted so that the dimples would be less deep, which it turns out was totally not necessary.  But, anyway, it's working.  My next picture will be of the completed model.

[homespun]

Whew!  That was quite a task!

[TaffGoch]

Hey, I did try to make it easier for you.

I expect you'll be taking a break for a while (maybe) ?

[homespun]

Yes, I go back to work next week.  It was fun to have made so many modles in these last few weeks.

                                                                    Dan

----- Original Message -----

From: TaffGoch

To: geodes...@googlegroups.com

Sent: Friday, January 18, 2013 1:32 PM

Subject: Re: Geodesic Dome Origami - Believe It!

Hey, I did try to make it easier for you.

I expect you'll be taking a break for a while (maybe) ?

--

[homespun]

Two more pictures of model just before I closed it up.