zif molecule

[TaffGoch]

From: marcos lutyens
Date: Thu, Sep 3, 2009 at 7:47 PM
Subject: zif molecule
Dear Taff,

Your geodesic work is amazing..I found it in skecthup...

I am working on a large sculpture installation for the Royal academy, London based somewhat on a zif "carbon scrubbing" molecule  and was looking at making a carbon shell out of regular hexagons so that I can get approval of the engineers (a structure made of tubes does not seem to fly).  I was wondering if you could take a quick look at this shell and tell me if the hexagons can be regular or not (the problem of it resting flat on the ground does not apply as we are securing it off the ground)?  Also maybe you have  a better idea for a zif like geometry approach?

Thanks so much

Marcos Lutyens

[TaffGoch]

Marcos,

First point; if you use regular hexagons, then 6 of them, surrounding
a hexagonal hole, will be planar. You have to use slightly irregular
hexagons to get them to lie on a spherical "surface."

As far as art/sculpture, I'm sure that no one would be able to discern
that the hexagons aren't regular.

Were you thinking of metal panels? Perhaps, like tiles or slabs?

Taff

[marcos]

I see...well, I was hoping that the hexagins were regular as I
intended making the pice from one mould.

I am looking into fabricating the tiles out of carbon fiber, and was
looking for an easy or interesting regular tesselation...

Marcos

[TaffGoch]

Don't misunderstand -- as long as you don't try to attach them too "intimately," you can, indeed, get away with regular hexagonal tiles. While you can't connect them in a circle around a small (single hexagon) hole, you can string them together in patterns that surround a larger, or irregular "holes."

 

I'll look through my models, to see if I can find an example that depicts something similar.

 

Taff

[marcos]

so if I slope the edges appropriately and then bolt the tiles together
it will begin to give me the required arc..?
The holes openings in my model may help to "fudge" the geometry in
other words?

Yes, I'd love to see any geometry that fits the zif better and yet is
made of regular tiles if possible!

[TaffGoch]

The "holes" should provide the "wiggle room" you need to use identical tiles. However, if you use regular hexagons, and you attach three to each other (not in a straight line,) then that, too, would be planar. You're going to have to avoid that arrangement, as well.

 

If I'm reading the email header properly, you're in the Pacific time zone(?) If so, I'm a couple of hours ahead of you, and will likely have to postpone the posting of example(s) until tomorrow.

 

Taff

[marcos lutyens]

Well I look forward to seeing the models tomorrow...

I think that should help for now...thanks so much!

marcos

[TaffGoch]

Marcos,

 

Here's a quick example of regular hex tiles, arranged on snub-dodecahedron geometry. Food for thought....

[marcos lutyens]

that's an intriguing stab at the issue...

what would the geometry look like if one added as a repetition just one other slightly differently shaped hexagon type?  

[TaffGoch]

A couple of hexagons (both slightly irregular) can be tiled along
icosahedron/dodecahedron rotational symmetry, opening up many
possibilities.

Tomorrow, though ... (bedtime)

[marcos lutyens]

another approach, since we can only fit an arc of a sphere above the portico, and we need smaller openings to generate a solid enough structure as per the engineers, would be a geometry like that derived from the  the snub-dodecahedron, but with more facets ...does that exist ?

do-deca= 12  double-do-deca = 24?

I'd be intrigued to see the possibilities once you wake !

Thanks for the insights!

[Adrian Rossiter]

Hi Marcos

On Thu, 3 Sep 2009, marcos lutyens wrote:
> another approach, since we can only fit an arc of a sphere above the
> portico, and we need smaller openings to generate a solid enough structure
> as per the engineers, would be a geometry like that derived from the

I'm not exactly sure of your constraints, but you can build
a rigid dome from regular hexagons by taking a section
between two hemispheres from the quarter cubic honeycomb
(discarding the triangles)

http://en.wikipedia.org/wiki/Quarter_cubic_honeycomb

Here is a thin shell as an example

http://www.antiprism.com/misc/hex_dm01.jpg

If you make the shell thicker all the hexagons can be bonded
by edges, and at some thickness it will become rigid.

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

[marcos lutyens]

Hi Adrian,  

That is indeed ingenious..however we also need to make an array of openings to get a little closer to the "spirit" of the Zif molecule which by the way has been developed by the very talented Prof Omar Yaghi at UCLA  http://yaghi.chem.ucla.edu/

The challenge for us is that the molecular forms are on the whole very spindly and difficult to build to withstand wind loads etc...that is why we have been looking for a geometry rather like what Taff sent yesterday that forms the solid basis for our form.

Marcos

www.mlutyens.com

[Adrian Rossiter]

Hi Marcos

On Fri, 4 Sep 2009, marcos lutyens wrote:
> Hi Adrian, That is indeed ingenious..however we also need to make an array
> of openings to get a little closer to the "spirit" of the Zif molecule which
> by the way has been developed by the very talented Prof Omar Yaghi at UCLA
> http://yaghi.chem.ucla.edu/

You could make holes by leaving out faces.

> The challenge for us is that the molecular forms are on the whole very
> spindly and difficult to build to withstand wind loads etc...that is why we
> have been looking for a geometry rather like what Taff sent yesterday that
> forms the solid basis for our form.

It isn't like Taff's model, but here is another model that
might be of interest as it is spindly and rigid. It was made
by Daniel Suttin from from card octahedron and tetrahedron units
assembled with paper clips

http://farm4.static.flickr.com/3424/3353395373_188d2854f8_o.jpg

Although the shape apparently has icosahedral symmetry I think,
by the colours, the units were probably regular octahedra and
tetrahedra. Dan has some specially shaped octahedron and
tetrahedron units now for building shapes with 5-fold symmetry.

[marcos lutyens]

Daniel Suttin's work is stunning...What would the name of the structure be that you sent me on Flickr?!

It does seem to have the characteristics of a zif molecule in so far as it has larger and smaller openings with symmetry...

[TaffGoch]

Adrian,

 

I had not seen Suttin's constructs before.

 

I was going to suggest to Marcos that a hands-on modeling kit, of some kind, would be handy for exploring variations.

 

Here's some more pics...
http://images.google.com/images?q=Octa-Tetra

...and Suttin's algebra page about the kit:
http://www.homespun4homeschoolers.com/octa-tetra.htm

 

From the detail photo, the structure looks to be made of aluminum (nice reflectivity.) That, plus the fluorescent colors, makes for a pretty dramatic presentation.

_____________________

 

Marcos, I can see regular pentagons (holes,) which are a dead give-away that the underlying structure is icosahedral (dodecahedral).

[TaffGoch]

Adrian,

 

You're right, it's just cards and paperclips!

(I can see the clips in the detail photo.)

[marcos lutyens]

Hi Adrian and Taff,

Is there a digital way of working out the strut/side lengths for  a form like that?

So I can unfold the piece and see how it is made , how many components are needed etc...

Thanks so much,

Marcos

[TaffGoch]

Marcos,

 

The Suttin construct shares the rotational symmetry of an icosahedron/dodecahedron (or, a soccerball/buckyball.)

 

You can count components from the photo, for representative faces, then multiply by the pentagonal faces (12) and the triangular faces (20.)

 

The yellow components are tetrahedrons, while the pink ones are octahedrons. (The octet-truss is fairly-commonly used in architecture nowadays.) Your engineers should be comfortable with the concept.

[TaffGoch]

Oops, I got it backwards,...

 

...the pink ones are tetrahedrons - the yellow ones are octahedrons.

[TaffGoch]

This photoshopped color-correction should make it easier to count (yellow vs. pink)

[marcos lutyens]

so its 2 basic forms?  repeated in a specific array?

[marcos lutyens]

simple when you know how!

[TaffGoch]

This evening, I'll try to demonstrate how they're put together, in a SketchUp model.

 

(I've got to run some errands right now...)

[marcos lutyens]

look forward to that...

[Adrian Rossiter]

Hi Marcos

On Fri, 4 Sep 2009, marcos lutyens wrote:

> Is there a digital way of working out the strut/side lengths for a form
> like that?
>
> So I can unfold the piece and see how it is made , how many components are
> needed etc...

I am not sure if the shape has a particular name.

You have to be careful with measuring using the units as some
of the units will have been distorted slightly in order to
make the shape close.

Here is a model of the outer ring of one of the pentagons
before it has been made to close

http://www.antiprism.com/misc/oct_tet_ring_gap.jpg

Dan now uses some different units for models with 5-fold symmetry.
They come from a structure known as the Golden Octet Truss

http://www.kabai.hu/sites/default/files/GOT-a.doc

[TaffGoch]

I was SketchUp-modeling the Suttin sculpture, finding that same "gap" !

 

The flexibililty of card-and-clip construction likely allowed for the "fudging" required.

 

I'll have to test the golden-octet truss, to see if all similar components will permit pentagonal circuits. If not, then a combination of golden and true octet components may permit "buckyball" construction.

 

(Thanks for the reference, Adrian. I hadn't read before of the "golden octet.")

 

Taff

[marcos lutyens]

yes fudging is not possible at a larger scale with aluminum etc!

can you think of any form that is suggested by the openings in the attached file (ignore the curved surface)?

[TaffGoch]

Oh, man, after I did this ?!

[TaffGoch]

Marcos,

Kidding aside, I'll look at the original molecular images, and your
latest, and see what might be modeled that is suggestive.

Taff

[marcos lutyens]

that is really great...I am impressed  

is it called a "golden truncated gochohedron" by any chance?

[marcos lutyens]

or does suttin retain the credit?

[TaffGoch]

Actually, the "golden" octet was a guess, and won't "fix" this construction. A lot can be built with golden-octets, but not this particular sculpture.

 

I "constructed" this octet-truss model with regular octahedrons(840) and tetrahedrons(1740).

 

You can see the slight gap at each of the pentagonal corners. The corner elements could be modified to fit tight, making for a few (relatively speaking) additional "custom" pieces.

 

(I liked it enough that I made it my current wallpaper!)

 

Certainly, Dan Suttin is to be credited for the arrangement, but I wouldn't think that he's that jealous about "sole use." Actually, slight changes, here and there, would make the resultant arrangement "unique."

[TaffGoch]

Marcos,

 

Looking at your original images (first post,) I can see the underlying geometry for the "(a) poz B" configuration.

 

Compare the attached "truncated cuboctahedron" image to the stretched "(a) poz B" figure, and see if you can recognize the association.

 

Taff

[TaffGoch]

I can see the relationship between your latest image with the "(d) moz" configuration.

 

I'll see if I can find a polyhedral solid that resembles that one.

 

Taff

[marcos lutyens]

yes it is quite close, but the elongated elipsoid openings are curious at least to me, as I have not really seen this before....

[TaffGoch]

Marcos,

 

The geometry in your image can not be reproduced with an icosahedron subdivision (the typical geodesic dome.) While a geodesic dome generally has a 5-fold rotational symmetry, your image, and that of "(d) moz" exhibit 4-fold rotational symmetry, around all three primary axes.

 

I noticed that you are comfortable with modifying an icosahedral geodesic sphere, to experiment with your image. You should be able to better conform your image to the "(d) moz" geometry with the attached model, which breaks down a "truncated rhombic dodecahedron" into a sub-divided sphere. If you need smaller subdivision, let me know. This should, however, get you started with continued experiments.

 

There is no regular polyhedron that comes closer to "(d) moz" than does the truncated-rhombic-dodecahedron. I hope it helps.

 

Taff

[marcos lutyens]

Dear Taff,

That helps a lot...I think the 5 vs 4 fold rotational symmetry issue has been a key factor in trying to understand if a geodesic type structural  approach  can be superimposed into a form of 4 axis rotational symmetry!

We will update you as the project progresses!

Marcos