Simpler Floret Design

[TaffGoch]

Dan (homespun) may have been "put off" by his last floret construction, due to its size & complexity.

This floret sphere is smaller and easier to construct -- only 7 unique petals, rather than 13:

It's based on the dual of the Class-III {3,5} icosahedron tessellation.

(As pointed out previously, the rhombic hexecontahedron is the simplest icosahedral example of this "floret" style of composition.)

-Taff

[homespun]

Hi Taff,

    Too busy with other projects to play with this one right now, but please do post the pattern, and maybe I'll get to it someday.  If so, I will make it as small as possible; last time I went way too big.

                                  Dan

[TaffGoch]

Okay, Dan,

Here's the template, which can be scaled to fit a page for printing.

I've also posted the model at the 3D Warehouse...

http://sketchup.google.com/3dwarehouse/details?mid=3d6277b88fd59ec232df204703f4a765

...for readers who would like to examine with SketchUp.

-Taff

[TaffGoch]

Lesser frequencies modeled, as well:

-Taff

[homespun]

Taff,

   Please post templates for these two as well.

                     Thanks,

                      Dan

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

From: TaffGoch

To: Geodesic Help Group

[TaffGoch]

Dan, I will generate and post templates.

__________________________

For interested readers, these "floret" tilings are duals of snub tessellations of the icosahedron and triacontahedron.

The snub truncated icosahedron, and its floret dual (Conway notation: dstI)

The snub 5-truncated triacontahedron, and its floret dual (Conway notation: dst5daD):

The snub dual kis-5-truncated snub icosahedron, and its floret dual (Conway notation: dsdk5sI):

If you want to explore Conway notation, there is polyhedra generator at George Hart's webpage:

http://www.georgehart.com/virtual-polyhedra/conway_notation.html

-Taff

[TaffGoch]

...and the pentagonal hexecontahedron; the dual of the snub dodecahedron:

...being the simplest "floret" polyhedron, as pointed out by Katrina Fairley, in a previous discussion regarding floret tessellations.

-Taff

[TaffGoch]

I found these two floret spheres rather interesting:

Each icosahedron face (defined by the centers of the pentagonal florets,) is composed of 21 "petals" -- 18 hex and 3 pent petals. Note that in one, the pent-floret petals "point" straight-at the adjacent icosa vertices, while in the other, the pent petals point toward a position just off-center of the icosa face.

One of the "snub" triangular tessellations (these being the duals) is subdivided as Class-I, frequency 7v{0,7}. The other is Class-III, frequency 8v{5,3}. Both are composed of the same number of triangles (if you divide the hexagons and pentagons into their component triangles.) I haven't noted such an "identity" as this, before. Perhaps, it is not uncommon, but I haven't recognized it, previously.

I wrote that I found the floret patterns "interesting." Confounding might be the better description, when I was trying to model them in 3D.

-Taff

[TaffGoch]

I neglected to attach the "map" that I had prepared, depicting the differing icosa-face petal layouts:

[TaffGoch]

While producing these "Floret" tessellations, I "got lost," and had to organize the classification of which tessellations that I had done, and those that I wished to work on, subsequently.

I produced an orderly mapping of the floret tiling, showing the icosa faces for the different geodesic classes and frequencies. On the attached map, the frequency can be determined by counting from center of a floret, to the next floret center. These are the numerical labels beside each equilateral triangle. These are my own "namings," and I question that it appears elsewhere. It certainly isn't the only possible classification. Someone else may have produced something similar, with different labeling.

The red line represents a "mirror" edge. Examples of the shown triangles exist to the left of the red line, but aren't shown. (Note that I have produced a {1,2} and a {2,1} version, as depicted in my previous posting.) Those triangles that "split" the red line can be recognized as Class-II tessellations, while the bottom row are all Class-I. Those triangles that fall elsewhere (in between) are Class-III tessellations.

Interestingly, some arrangements can not be classified by Conway notation. I have used both, George Hart's online Conway notation javascript applet, and Adrian's "Conway" program, to generate cartesian coordinates. At least one, so far, required manual modeling of plane rotations and intersections (the {3,1} example.) If I'm wrong about this, I'd appreciate schooling from someone more familiar with Conway notation.

The green examples, I have completed. The red ones are on my "to do" list. First, I need to rename my completed model files, to correspond to my revised numeric labeling.

______________________________

What really made my "head explode" was the realization that there is a duplicate set, one-for-one, that reverses the depicted "spin" of adjacent florets in the underlying tiling pattern, while keeping the icosa triangle arrangement the same.

-Taff

[TaffGoch]

Here's the {1,3} version that I had to model manually (I previously erred in identifying this as {3,1} in the previous posting):

[TaffGoch]

For the curious, here's the relationship between the "snub" and "floret" tessellations (being duals of each other)

[TaffGoch]

I've finished populating the map:

I posted the SketchUp models at the 3D Warehouse; putting them in a collection, that they may all be found in one place:

http://sketchup.google.com/3dwarehouse/cldetails?mid=a026cd04804def0d86509ade26108092&num=15

-Taff

[Dick Fischbeck]

Taff

I passed this on to Joe Clinton. I'll send you any response he has.

Here's a sail-by past Bear Island from last weekend, just for fun. Best in HD. Camden Hills in the background.

https://www.youtube.com/watch?v=EPpQfhVt_3M

Dick

-Taff

--
 

[TaffGoch]

Thanks, Dick, for sharing with Joe Clinton.

__________________

To clarify symmetry relationships, I produced a 3D model that depicts the chiral nature of the Class-III, 3v tessellations. (Nothing new to those familiar with Class-III.)

What IS different is that I also mirrored the floret pattern, depicting it's chiral opposite, as well. This introduces two new tessellations, producing a total of four distinct Class-III, 3v, floret tessellations:

I needed some means to categorize and distinguish the difference in tessellations, so I introduced "dextro/laevo" labeling, specific to the rotation of the floret pattern. The clockwise (dextro) and counter-clockwise (laevo) floret association (any three adjacent florets) is depicted as such:

_____________________

By the way, online, I have noted inconsistencies in the {m,n} subdivision labeling of Class-III tessellations. Some sources count edge subdivisions clockwise, while others followed a counter-clockwise "route." For the {m,n} categorizations in the above images, and in my 3D models, I use the convention employed by Popko, in his book, "Divided Spheres." When counting, from floret-center-to-floret-center, I always "turn left" when jogging a path from an icosahedron vertex to the next. It's easy for me to remember, by thinking "NASCAR" -- always turning left. This is applicable to these floret tessellations, as well as any triangular Class-III tessellation.

-Taff

[homespun]

Taff,

   I have saved every picture from this thread into a special file.

   Still hoping you will get around to posting the templates for the two "lesser frequency" models.

                                                                 Dan

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

From: TaffGoch

To: Geodesic Help Group

Sent: Monday, August 05, 2013 9:29 PM

Subject: Re: Simpler Floret Design

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[TaffGoch]

Dan,

Look through the different versions, and let me know which one(s) you want to construct. I'll make templates for those that you specify.

-Taff

[homespun]

These two I have attached...

            Thanks,

                Dan

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

From: TaffGoch

To: Geodesic Help Group

Sent: Monday, August 05, 2013 10:11 PM

Subject: Re: Simpler Floret Design

Dan,

Look through the different versions, and let me know which one(s) you want to construct. I'll make templates for those that you specify.

-Taff

--

[TaffGoch]

Got it; will start process...

[TaffGoch]

Dan,

Here's the dextro{1,1}:

[TaffGoch]

...and here's the dextro{2,0}:

[TaffGoch]

Darn it, I'm still getting dextro & laevo mixed up!

The template I posted for the {2,2} model was laevo, while the depicted sphere was dextro. You can flip the template, or use this:

It's probably better to use these, considering that you archive images in your museum documentation. (Disregard/throw-out the previous!)

-Taff

[TaffGoch]

Boy, I wish there was a way to edit posts -- My last post depicted (2,0}, not {2,2}...

[Adrian Rossiter]

Hi Taff

On Fri, 2 Aug 2013, TaffGoch wrote:
> Interestingly, some arrangements can not be classified by Conway notation.
> I have used both, George Hart's online Conway notation javascript applet,
> and Adrian's "Conway" program, to generate cartesian coordinates. At least
> one, so far, required manual modeling of plane rotations and

> intersections *(the
> {3,1} example.)* If I'm wrong about this, I'd appreciate schooling from

> someone more familiar with Conway notation.

As regards operations, you can apply gyro with an optional reflect
to a general geodesic sphere.

In Antiprism, you can make the four "3,1" variations like this

conway g geo_1_3 | off_color -f S -m rng16 | antiview
conway rg geo_1_3 | off_color -f S -m rng16 | antiview
conway g geo_3_1 | off_color -f S -m rng16 | antiview
conway rg geo_3_1 | off_color -f S -m rng16 | antiview


Regarding your following post on the meaning of the numbers. I
don't define in Antiprism what it means to be 1,3 rather than
a 3,1 in geometric terms. The division is applied to a surface
made of oriented faces, and reorienting the faces flips the
pattern. E.g. a 1,3 pattern applied to a "positively" and
"negatively" oriented icosahedron produces models which are
mirrors of each other

off_util -O p ico | geodesic -c 1,3 | antiview
off_util -O n ico | geodesic -c 1,3 | antiview

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

[Dick Fischbeck]

Boy, I hear you! I'm always shooting off posts too quickly.

[TaffGoch]

Thanks, Adrian, that makes sense with your program.

My problem was that, as far as I can tell, "1,3" or "3,1" is not supported in strict Conway notation. Your program adds the "geo_m_n" option. (Much appreciated, by the way.)

So, is it correct to assert that one can not produce a 1,3 tessellation, using strictly "native" Conway notation?

-Taff

[Adrian Rossiter]

Hi Taff

On Tue, 6 Aug 2013, TaffGoch wrote:
> My problem was that, as far as I can tell, "1,3" or "3,1" is not supported

> in strict Conway notation. Your program *adds* the "geo_m_n" option. *(Much
> appreciated, by the way.)*

>
> So, is it correct to assert that one can not produce a 1,3 tessellation,
> using strictly "native" Conway notation?

If you use a minimal Conway Notation then I don't believe you can
produce a 3,1 geodesic icosahedron.

To prove this, notice that all the operations multiply the number
of edges by a factor from the range 1-6

http://en.wikipedia.org/wiki/Conway_polyhedron_notation#Operations_on_polyhedra

A 3,1 icosahedron has 390 edges, which has 13 as a prime factor.
This factor could not be introduced by operations so it must
have been a factor of the number of edges of the seed. The only
possibilities are Y, A or P with at least a 13-fold axis, but as
the geodesic icosahedron does not have an axis greater than 5-fold
these are discounted.

More generally there is freedom to choose the seed, hence I
started with a 3,1 geodesic icosahedron. The set of operations
may also been extended ("reflect" is an example), but the
geodesic pattern operation doesn't really fit into Conway Notation
operation, because it requires the tiling to be all triangles. A
tringulation operation could be incorporated, but that would be
messy as there would no longer be good formulas for the resulting
number of faces, edges and vertices.

[TaffGoch]

Thanks, Adrian,

I had referred to that wikipedia resource many times, in my explorations. The explanation of the "seed" is minimal. 

George Hart's Conway interpreter (http://www.georgehart.com/virtual-polyhedra/conway_notation.html) only accepts Platonic solids and Y(pyramid,) A(antiprism,) and P(prism) for the seed. Your explanation clarifies why I couldn't "get a foot-hold" in my geodesic {1,3} attempt.

I esteem your enhanced "Conway" program (http://www.antiprism.com/programs/conway.html)

________________

I "enhanced" my comparison model, to include depictions of the four different snub duals of the floret tessellations (attached.)

-Taff

[TaffGoch]

For those readers interested in studying Conway notation, you might find useful a "prettified" poster (attached) that I produced during my own explorations.

Note that the "g" (gyro) parameter can be used, to substitute for some of the "snub/dual" parameters. I kept it simple, to avoid (my own) confusion.

As posted earlier, George Hart's webpage, "Conway Notation for Polyhedra" (http://www.georgehart.com/virtual-polyhedra/conway_notation.html) is a useful tool for study. There is also a wikipedia page on Conway Notation, but be forewarned that there are a some errors in a few polyhedra parameter strings.

I found that Hart's VRML generator did not work in my internet browser (Chrome.) Be sure to download and experiment with Adrian Rossiter's "Conway" program, in his Antiprism collection (http://www.antiprism.com/programs/conway.html)

-Taff

[TaffGoch]

Recent Chicago architecture competition, "Chicago Center for Permaculture and Appropriate Technology" (C4PAT):

http://lbccchicagocompetition.wordpress.com/

Hmmm, seems familiar, somehow....

Their "C4PAT" logo:

-Taff

[homespun]

Taff,

   Two questions:

        Did they get the idea from Geodesic Help?

        When I did my paper model, it was really flimsy and tended to collapse under its own weight?  How do they avoid such problems?

                                 Dan

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

From: TaffGoch

To: Geodesic Help Group

Sent: Sunday, August 25, 2013 5:56 PM

Subject: Re: Simpler Floret Design

--

[Camilla Fox]

What scale are you doing paper models at? If I do solid, I tend to aim for pieces an inch in diameter, and to put a tab on every edge of every face, so the two tabs stick inwards and contribute to stability. Out of 65 or 130lb cardstock, that will be fairly sturdy to volley-ball sized, and at baseball-sized you can toss it across the room without harm. With a mostly-hexagons type model, the stability problem will be that corners that pop inwards easily.

Edge models like this one: http://web.mit.edu/cfox/www/spherical-models/2002-05-10/index.html (yeah, been a while since I touched it, old web page) are very crisp and sturdy, especially with a coat of paint. That's also in fairly lightweight cardstock, probably 65lb, since the edge models have much more precise cutting requirements and I found cutting them out (by hand) was tiring in the thicker stuff. (These florets have me feeling inspired, but my stuff is all on the back burner... my friend has a Silhouette craft cutter, and I hope to spin up on using that to make one of these.)

-Camilla

[TaffGoch]

Dan,

More likely, sourced from the 3D Warehouse:

http://sketchup.google.com/3dwarehouse/details?mid=2958385a4dbed04294d3b6d776085e61

Your second question is the "more-meaty" discussion topic. It has been documented that higher-frequency domes are, indeed, more susceptible to "pop-in" (inversion, buckling,) than are lower-frequency domes, when using comparably-sized members/panels.

Your cardstock model demonstrates that thin material, relative to the size of the model, is an unwise choice (but you're now wiser for the experience, eh?) As I'm sure you've noted from origami, a paper or card, folded sharply, is stronger than a shallow-folded example. Mechanically, this property scales-up, to real-world examples.

When compared to a low-freq dome, a high-freq dome often requires "thicker" struts AND joints (since joint failure is the more prevalent.) If the Chicago permaculture dome is ever built, it will singularly-depend on struts/hubs for structure, similar to the Eden Project domes.

In "panel" domes, where there are no individual struts or hubs, the shallow dihedral angle of high-frequency subdivision can doom the structure to failure. This characteristic demonstrates one of the advantages for "pyramid-peaked" triangular panels. The dihedral "folds" can be made "sharper," thereby decreasing the chance of a fold inverting, or buckling, when subjected to localized loads.

[BTW, the "pyramid-peaked" triangles of Epcot's "Spaceship One" are veneer, providing no structure. They are merely attached to the outside of the structural geodesic sphere, hidden underneath.]

[TaffGoch]

Dan,

Immediately, upon seeing this photo, thought of your octet constructs....

[homespun]

Taff,

   That picture is contained in a file I did back in 2007, #142, now am up to #650 and beyond.  See attached.

   It's a Word file; let me know if it opens OK.

                    Dan

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

From: TaffGoch

To: Geodesic Help Group

Sent: Monday, August 26, 2013 9:26 PM

Subject: Re: Simpler Floret Design

Dan,

Immediately, upon seeing this photo, thought of your octet constructs....

[homespun]

My model can be seen at:  https://www.facebook.com/photo.php?fbid=393898010677071&set=a.250289648371242.60107.250284981705042&type=3&theater

                Dan

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

From: TaffGoch

To: Geodesic Help Group

Sent: Monday, August 26, 2013 6:17 PM

Subject: Re: Simpler Floret Design

 

.........Your cardstock model demonstrates that thin material, relative to the size of the model, is an unwise choice (but you're now wiser for the experience, eh?) As I'm sure you've noted from origami, a paper or card, folded sharply, is stronger than a shallow-folded example. Mechanically, this property scales-up, to real-world examples.............

 

[homespun]

Taff,

   Did you find time to look at that file I sent with pictures from Montreal EXPO '67?

[TaffGoch]

Yes, it opened okay.

I've also visited your facebook page/albums, several times over the past few months.

[TaffGoch]

Another architectural geodesic floret tessellation (pentagonal hexecontahedron,) spotted online...

...being a proposed Amazon headquarters design, for Seattle:

 (Aug 20, 2013)  http://www.gizmag.com/amazon-hq-update/28750/

A previous (declined) proposal was not icosahedron-based:

http://www.architizer.com/blog/amazons-new-biospheres-show-techs-link-to-hippie-dippie-1960s/

[homespun]

Wow, That is beautiful!

                Dan

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

From: TaffGoch

To: Geodesic Help Group

Sent: Friday, August 30, 2013 3:26 PM

Subject: Re: Simpler Floret Design

[homespun]

Taff,

   I would very mush like to make a cardstock model of one of these pentagonal hexecontehedra in the style of Amazon-Seattle with closed "solid" modules.   There are three separate modules:

                1)  the main pentagonal module

                2)  a 5-hub

                3   a 3-hub

 

                      

Could you make me patterns for those at some time in the near future?

 

I would like it to be one of those curved-fold papercraft models like this one. 

 

 

 

 

Is it possible?

 

                                         Best wishes,

[TaffGoch]

Dan,

I suspect that a curved-fold version is not practical/possible.

Out of personal interest, I started on a digital model, composed of geodesic triangles:

Right now, it's a single layer, rather than a truss, as depicted in the Amazon images. I hadn't considered making it "thicker" by adding the second interior layer, connected by a "holed strip." (It was time-consuming, as is.) If I were to attempt the task, it would not be "spherical" surfaces, but adjoined triangles.

-Taff

[TaffGoch]

Here's what I meant about it being "adjoined triangles"....

-Taff

[homespun]

Taff,

    Thanks for considering my request.  But the question remains,-- How dod they do it and have an interior second layer, and yet make it spherical?

    I really want to build it.

                                                                                    Dan

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

From: TaffGoch

To: Geodesic Help Group

[TaffGoch]

Dan,

Their initial design is established by the geometry of the pentagonal hexecontahedron, but ultimately-refined and fabricated of spherically-formed plate or welded-up spherical pieces. 

I'm restricted to flat faces; that being a limitation of SketchUp. I subdivided the pentagonal faces, into 7 triangles. I could more-closely approximate a sphere, by further geodesically-subdividing the triangles; x2 or x4, etc.

A paper model could have curved "arms," but the central pentagonal region would be flat. If a cut is made, in the central region, the paper could be formed into a shallow cone, to more-closely approximate a spherical surface.

-Taff

[TaffGoch]

Dan,

This "lampshade" is the same geometry, and is sold disassembled. The 60 identical pieces are apparently made of stiff, but somewhat-flexible plastic, with punched holes at the nodes.

You could start with this simple design, and further embellish it, as did the Amazon architects.

-Taff

[TaffGoch]

Dan,

Should you wish to pursue....

[homespun]

Just playin' around.....tedious and flimsy......don't know if I will pursue......

[TaffGoch]

Dan,

For heavier cardstock, perhaps....

(I customized this to ensure 72° at the top vertex, and 120° at each of the others, so it should produce "flat" regions at the vertices. If the cardstock is sufficiently heavy, 60 of these should provide a sufficiently-spherical approximation.)

You could leave the "holes" intact, to improve rigidity -- coloring them after assembly, maybe.

-Taff

[TaffGoch]

Dan,

BTW, since the pentagonal hexecontahedron has faces that exhibit mirror symmetry, down the middle. it shouldn't make any difference whether you connect the five-fold "clusters" of faces clockwise or counter-clockwise.

The pentagonal "clusters" can be assembled either way 'round. (This is not true for higher-order floret tessellations.)

-Taff

[homespun]

Taff,

   Have started over with new template.  So far, so good.  Will send picture when three florets completed.

               Thanks,

[TaffGoch]

I finished "fleshing out" the spherical form of the pentagonal-hexecontahedron superstructure, and added the planar glazing, as depicted in the architectural proposal. Here's a depiction of the welded-up steel superstructure:

The SketchUp model (238kb,) with the glazing in a separate layer, is available at the Trimble/Google 3D Warehouse:

http://sketchup.google.com/3dwarehouse/details?mid=f02696846822e06124377aac91b864b1

-Taff

[homespun]

Taff,

   That's the model I'd really like to make if it were possible, with the two layers, but I guess I will have to be satisfied with just one layer.  I should have a progress-report picture for you in two or three hours from now.

                                           Dan

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

From: TaffGoch

To: Geodesic Help Group

Sent: Monday, September 02, 2013 5:00 PM

Subject: Re: Simpler Floret Design - Pentagonal hexecontehedron

--

[homespun]

Taff,

   Here it is with 3 of the 12 sections completed.  I shall continue on it in the evenings of this coming week.

                                        Dan 

 

[JRal]

Hi Dan 

Here is a Lampshade piece I made a while back when I first started playing with domes,  Sorry the pictures are a bit rough. I had no idea what I was doing and simply copied the distances to the verticies/ joining points from a picture I saw online somewhere, I added the opposing C curves 'S" to make it my unique design; although I'm sure someone somewhere has done this variant before. 

I never figured out how the geometry worked, Now I have to go back through this post and get my head around it.

This is what got me onto doing the curved plywood dome that is currently sucking all my time.  

I ended up replacing the CFL bulb with a halogen bulb in to get nicer shadows, I couldn't find any pictures of this and I have to wait to tonight when it is dark to take another one.  

John 

[homespun]

JRal,

    Cool!.....

    And I have saved all the pictures you have sent on the "curved plywood dome".

                            Dan

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

From: JRal

To: geodes...@googlegroups.com

Sent: Tuesday, September 03, 2013 7:52 PM

Subject: Re: Simpler Floret Design - Pentagonal hexecontehedron

[TaffGoch]

John,

Yes, indeed, your lampshade is based on pentagonal-hexecontahedron symmetry. It goes to show that the faces don't, necessarily, need to depend on mirror symmetry.

I wish there were some way to search online for such lamps. I'm sure there must be others....

[TaffGoch]

All the variations that I can find have been the work of David Trubridge:

I was thinking about making a "random," or fractal/chaos, tree-branch variation, but the above demonstrates that he's already done that!

-Taff

[John Ralphs]

Here is a better shot with the halogen bulb in.

After I made the lampshade I tried to figure out the geometry, I got as far as figuring out it was a dual of a snub dodecahedron, but I couldn't figure out how to increase the frequency. Now I have read through all the post I have a much better idea about how to do it.

With the help of Taffs wonderful library of models in the SketchUp 3D warehouse, I'm going to give something with a higher frequency a shot using the same construction method of overlapping and pinning all the vertices as used on this lampshade.

If that works I will change the construction method to the same as I am using for the curved plywood dome, being multilayered and overlapping at the joins. That won't be for a while yet though. I think a larger scale higher frequency variation (possibly a tree branch style like in the first attachment of the previous post) of this would be amazing, I just need a wealthy sponsor to buy all the materials and time on a CNC router. :-)

John  

 

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[TaffGoch]

Dan,

If I recall correctly, you've been engaged in exploration of origami from "Modular Origami Polyhedra"

Note the cover image, in the top right corner. There's the pentagonal-hexecontahedron geometry of the Amazon biodomes.

-Taff

[homespun]

Hi Taff,

   It shows that the "gyroscope modules" make the Catalan Dual of the Snub Docecahedron, the Pentagonal Hexecontehedron.  It is a model I have made and have on display at my Museum.

   I sent pictures of the drawings of Amazon /Seattle HQ to Rona Gurkewitz which she was excited to see. 

   My model will be finished tomorrow, and I will send you pictures. 

                 Dan 

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

From: TaffGoch

To: Geodesic Help Group

Sent: Friday, September 06, 2013 10:12 PM

Subject: Re: Simpler Floret Design - Pentagonal hexecontehedron

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[homespun]

Here it is:

 

 

      Dan

[homespun]

Here it is installed at my "Museum":

   

 

 

                                     Dan

[TaffGoch]

Great! I was worried that the stock would be too flexible, and that it would fold in upon itself. I'm glad to see that it holds form. (I hope the humidity, down there, doesn't do it in.)

_________________

Have you ever tried other materials? In the "cosplay" world, many costumes are made from foam floor mats....

...which can be "molded" if desired, using a hair dryer or heat gun. This webpage demonstrates a little bit:

http://nononsensecosplay.tumblr.com/post/12037955132/making-armor-using-foam

    

That webpage is one-of-hundreds available for reference, online, including youtube. I can foresee many uses for the material/technique, other than cosplay.

I imagine that the Amazon biosphere superstructure would nicely lend itself to modeling in this material. I'm putting this on my list of potential projects to pursue, while "shut in" this winter, 

-Taff

[homespun]

Taff,

   Cardstock worked well.

   I sent pictures to the architects, NBBJ - to their media person and their science/education person.  Told them I liked the design so much I just had to make a model.  (And, of course, I gave you the credit for making the pattern for me.)  We shall see if I get a response.

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

From: TaffGoch

To: Geodesic Help Group

Sent: Saturday, September 07, 2013 6:44 PM

Subject: Re: Simpler Floret Design - Pentagonal hexecontehedron

[John Ralphs]

I started on a card model of the Floret {2,1} pattern. 

Here is one piece, I need to change to a thicker card stock to make a full dome. I was also thinking of adding more sideways curvature to the struts to get rid of some of the mass in the centre of each piece to make it a little more elegant.  

I need to come up with a better labeling system as well as it gets quite confusing trying to figure out where to attach parts from here. 

I will be putting this on hold for a little while as I have my other project to get finished first.

John

[homespun]

John,

   So pretty!

      Dan

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

From: John Ralphs

To: geodes...@googlegroups.com

Sent: Monday, September 09, 2013 6:50 AM

Subject: Re: Simpler Floret Design - Pentagonal hexecontehedron

[homespun]

Taff, --

     Well, I decided I had to see if I could make the model, or at least part of it, with the 3 modules and with 2 layers.  I didn’t have an exact pattern for the size of the inner layer, how much smaller I should make it to get the proper curvature, and how far apart the layers should be, -- so it was all “guesswork”.

 

 

 

     And then I discovered that I had made the main module, the brown one, one segment too short on its long arm, and so I had to extend it.

 

 

   And here it is, or as much of it as I am going to do.  It’s rather crude, but it works, sort of.  Anyway, this is how I envisioned the model when I saw the first pictures of the plans for Amazon/Seattle.

 

 

 

                                                                                                                     Dan

 

P.S. The architects did not respond to my mesage and pictures....

 

 

[TaffGoch]

Dan,

With the full model that you've already built, you have an advantage. If you figure the "thickness" of the "box-style" component that you want, and compare that thickness to the full-model radius, you can calculate the percentage. Use that percentage for printing the smaller "inside" face.

For example, if the thickness is calculated to be 3% of the full radius, then you'd print the inner-face at 97% of the outer-face size.

The curved "edge" strips? I wonder whether they would simply follow the two sphere radii, inner & outer, producing a simple arc. To be absolutely certain, I need to "unwrap" that portion of the digital model (which I will do, now.)

I have to confess, yours is looking to be an enticing exercise.

-Taff

[TaffGoch]

The boxed-edge surfaces, when unfolded, do, indeed, follow the arc of the sphere radius....

[TaffGoch]

When you print the face pattern, you can determine the sphere diameter, based on the depicted ratio. Inversely, you can decide on the sphere radius, and from that, establish the size the pattern needs to be. (This is the outer face pattern ratio):

[homespun]

Taff,  Thanks so much for all your work on this project.

Here is the little piece on display at the Museum.

https://www.facebook.com/photo.php?fbid=559688880764649&set=a.250289648371242.60107.250284981705042&type=3&theater

                   Dan

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

From: TaffGoch

To: Geodesic Help Group

Sent: Thursday, September 12, 2013 9:46 PM

Subject: Re: Simpler Floret Design - Pentagonal hexecontehedron

When you print the face pattern.......

[David Reed]

I like this design. I noticed you have a dome to egg plugin. Will it work on this? I have access to a 24 x 18 laser cutter and was wondering if this can be adapted  so i can make a plastic model.

On Saturday, August 31, 2013 3:31:27 PM UTC-6, TaffGoch wrote:

Here's what I meant about it being "adjoined triangles"....

[TaffGoch]

David,

I don't have an dome-to-egg plugin (nor a sphere-to-egg plugin)

I have used, however, in building other 3D models, a "taper" transformation -- one of several transformation tools in FredoScale

That's the only thing I can bring to mind, to which you might be referring. You might find Fredo's plugin will do what you want. 

Note, however, that the Fredo transformations "break" groups/components, since these transformations were not built-in to SketchUp definitions/specifications. (The breaking of a component definition makes sense, if you study the internal formats of SketchUp. There's really no way to perform transformations, other than translation and uniform scaling, without "breaking things.")

Nice thing is, though, FredoScale lets you bend, taper, shear and twist things (which you, normally, can't do in native SketchUp.)

-Taff

[David Reed]

OH ok i went back to the post and it does refer to a plugin called freescale. ill look into it. I was thinking this would look nice in a egg shape even though it would have differing parts.

heres the old link

https://groups.google.com/forum/#!topic/GeodesicHelp/HNU2P-LLlUo

[Adrian Rossiter]

Reviving an old thread, I saw a dome on the Watchmen series that was very like the Amazon floret dome, but had pentagons bonded to each other on the "base" edges. It wasn't immediately obvious how to model the geometry, but I came up with a fairly close  model using the Antiprism conway program

   conway jdGD | canonical | off_color -f S | antiview

Adrian

P.S. I noticed some posts in the thread on multimodular origami polyhedra. I have written a form finding program for these

http://www.antiprism.com/examples/200_programs/720_mmop_origami/index.html

On Friday, 30 August 2013 at 22:26:25 UTC+2 TaffGoch wrote:

Another architectural geodesic floret tessellation (pentagonal hexecontahedron,) spotted online...

...being a proposed Amazon headquarters design, for Seattle:

 (Aug 20, 2013)  http://www.gizmag.com/amazon-hq-update/28750/

A previous (declined) proposal was not icosahedron-based:

http://www.architizer.com/blog/amazons-new-biospheres-show-techs-link-to-hippie-dippie-1960s/

[uncledan homespun4homeschoolers.com]

Adrian,

I would like to build this model with paper.  Are the red ones rhombi or are they kites?  Can you tell me some realtive dimensions and angles to work from?

     Thanks,

      Dan

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[Adrian Rossiter]

Hi Dan

On Thu, 2 Jun 2022, uncledan homespun4homeschoolers.com wrote:
> I would like to build this model with paper. Are the red ones rhombi
> or are they kites? Can you tell me some realtive dimensions and angles
> to work from?

The colours indicate symmetrically equivalent faces, but the red ones
around the 3-fold axis are mirrored.

Display some face and vertex numbers

conway jdGD | canonical | off_color -f S | antiview -n vf

Face 62 is green, 63 red, and 64 yellow. Lets get angles and edge
lengths for these faces, to 8 significant digits

conway jdGD | canonical | off_color -f S | off_query -d 8 -I 62,63,64 Fal

62,128.48871 80.55429 70.402714 80.55429,0.2337192 0.36516585 0.36516585 0.2337192
63,65.445975 115.06652 58.852674 120.63483,0.2337192 0.25679988 0.24973596 0.22665528
64,117.63665 62.363351 117.63665 62.363351,0.22665528 0.22665528 0.22665528 0.22665528

This is the face number, followed by the angles, follwed by the length
of the edge following each of these angles

This is clear for the green (62) kites and the yellow (64) rhombi.

The red (63) faces are neither kites nor rhombi, and we don't know
where on the face the angle and edge report starts, nor in which
direction. Rather than infer it, we could add the vertex numbers to
the report for this face

conway jdGD | canonical | off_color -f S | off_query -d 8 -I 63 Fval

63,16 109 73 196,65.445975 115.06652 58.852674 120.63483,0.2337192 0.25679988 0.24973596 0.22665528

This says the first angle (65.445975) is at vertex 16, and the first
length (0.2337192) is between vertices 16 an 109. The next angle
(115.06652) is at vertex 109 and the next length (0.25679988) is
between vertices 109 and 75. Etc. These quadrilaterals come in
mirror pairs, so when assembling the model half will need to be
flipped over.

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

[uncledan homespun4homeschoolers.com]

Adrian, thanks so much. 

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