A Kruschke Model of Your Own

[Paul Kranz]

Print these out on card stock, cut out, and tape together. A Cricut would help!

Very high regards,

 

Paul C. Kranz, LMFT

Kranz & Associates, LLC

ReviveTheFlame.com

[Dx G]

Nice model, although...suggestion.  I usually put a flange on each triangle edge where it will join another cutout.  Just makes it easier to assemble.  I find a glue stick and a pair of tweezers work really well.

DxG

[Michael Adkins]

U don't happen to have a EPS of that?

[Dx G]

I don't have one handy, but here is a site that illustrates the simple concept.  The flange is on the diagram to show that it is part of the cut out triangle, but is folded to meet the flange of the abutting triangle (basically dividing the dihedral angle in half when assembled).  If there are triangles in the diagram that are contiguous "on paper" and simply creased (at the dihedral angle) for fabrication, they don't need a flange. Its only for those triangles that need to be joined and have open space between them in the diagram.  This guy made all the triangles separately, so they all needed flanges. However, if he made his pentagons or hexagons out of just one flat piece of cardboard, there might only be one radial line in a given polygon where two triangle sides had to be joined, so the rest would be creased since they are already connected. Typically these mating flanges would be where the gathering angle made the flat pattern into an angled part when the two separated triangles are drawn together.

https://www.instructables.com/Cardboard-Geodesic-Dome/

If that is still vague, I likely could dig up additional illustrations if helpful.

-DxG

For people who think being "right" is proof of superior expertise, we in the research community always keep in mind that even a broken clock is right twice a day. 

--
--
You received this message because you are subscribed to the "Geodesic Help" Google Group
--
To unsubscribe from this group, send email to GeodesicHelp...@googlegroups.com
--
To post to this group, send email to geodes...@googlegroups.com
--
For more options, visit http://groups.google.com/group/geodesichelp?hl=en

---
You received this message because you are subscribed to a topic in the Google Groups "Geodesic Help Group" group.
To unsubscribe from this topic, visit https://groups.google.com/d/topic/geodesichelp/oht8KwmuL5g/unsubscribe.
To unsubscribe from this group and all its topics, send an email to geodesichelp...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/geodesichelp/d1707520-5428-4b66-8de3-b70aff648217n%40googlegroups.com.

[Dick Fischbeck]

Has anyone thought of using anything but face or edge elements to build a dome? Just wondering. I mean, there are 3 topological characteristics of a polyhedron. 

[Dx G]

Sounds like you have something in mind...care to elaborate?   Do your randomes qualify as face elements?  Not sure of the full meaning, just guessing.

DxG

--

--
You received this message because you are subscribed to the "Geodesic Help" Google Group
--
To unsubscribe from this group, send email to GeodesicHelp...@googlegroups.com
--
To post to this group, send email to geodes...@googlegroups.com
--
For more options, visit http://groups.google.com/group/geodesichelp?hl=en

---
You received this message because you are subscribed to a topic in the Google Groups "Geodesic Help Group" group.
To unsubscribe from this topic, visit https://groups.google.com/d/topic/geodesichelp/oht8KwmuL5g/unsubscribe.
To unsubscribe from this group and all its topics, send an email to geodesichelp...@googlegroups.com.

To view this discussion on the web visit https://groups.google.com/d/msgid/geodesichelp/CAG0f9gRDG7C1LkEq50GrLNPA2QSo%2B6rD729o7HiJg-fQOGWQxw%40mail.gmail.com.

[Dick Fischbeck]

No, not face, not edge. Vertex. I've thought about this switch for a long time and I can't find anyone who sees a difference. Thanks. 

You received this message because you are subscribed to the Google Groups "Geodesic Help Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email to geodesichelp...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/geodesichelp/CAF1iHD7UocUpaCTh3QbtBq58z3hrp7Oi8733hqbUW1n0vevYbQ%40mail.gmail.com.

[Dx G]

I'm sure there would be a difference.  It's the understanding part I'm after.  I figure faces would be a panelized dome, edges, perhaps a hub and strut dome. Vertex? I'm trying to keep an open mind. What would that be, how would it look or be designed or built?  I'm wondering if I'm missing something there.  Perhaps something worthwhile and potentially important?  You can only do the impossible if you can see the invisible...

DxG

To view this discussion on the web visit https://groups.google.com/d/msgid/geodesichelp/CAG0f9gRgs1VhzM841aLaKbEBv-XRWT%3DECMfb2vG%2B0qpLAV25UQ%40mail.gmail.com.

[Dick Fischbeck]

We can describe a face or an edge easily, as you do here. But what is the essence of a vertex?

The answer is, it is a structure that has an angular defect or deficit. It is a corner, or maybe we can say it is a conical structure, itself made of edges and face, 3 edges and 3 faces at minimum. The key is angle. Faces and edges don't have angles. 

This is food for thought. We are builders, after all. Think Euler.

Hope this helps general a discussion, and a model or two.

[Dick Fischbeck]

Well, faces can have angles, but only in 2 dimensions. Also, edges can be curved.

[Dx G]

Thanks for sharing your thoughts on this Dick.  Perhaps I misunderstand or oversimplify, but this is one way to look at it:

If you want to define flat faces, or a collection of angles, each face or angle would need 3 coordinates in space.

If you want to define a collection of lines or edges, each requires 2 coordinates in space.

If you want to define a collection of vertices only, each vertex is merely a single coordinate in space. 

However, if you want to define a collection of conical surfaces, these would be faces, each defined by the equation for that cone or section of a sphere. 

Am I missing the point...?  Not sure I'm getting what you propose.

DxG

--
--
You received this message because you are subscribed to the "Geodesic Help" Google Group
--
To unsubscribe from this group, send email to GeodesicHelp...@googlegroups.com
--
To post to this group, send email to geodes...@googlegroups.com
--
For more options, visit http://groups.google.com/group/geodesichelp?hl=en

---
You received this message because you are subscribed to a topic in the Google Groups "Geodesic Help Group" group.
To unsubscribe from this topic, visit https://groups.google.com/d/topic/geodesichelp/oht8KwmuL5g/unsubscribe.
To unsubscribe from this group and all its topics, send an email to geodesichelp...@googlegroups.com.

To view this discussion on the web visit https://groups.google.com/d/msgid/geodesichelp/CAG0f9gSt7qp7UwgNEWEcSa%3DwR8mc1q%2BC6ra%2B-Fyi3CodL8Sc3A%40mail.gmail.com.

[Dick Fischbeck]

Changed subject to vertex.

Basically, I'm saying there is a third way to build a dome. One purpose of doing this is that it is infinitely simpler. 

You received this message because you are subscribed to the Google Groups "Geodesic Help Group" group.

To unsubscribe from this group and stop receiving emails from it, send an email to geodesichelp...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/geodesichelp/CAF1iHD7AL7kRnLwkCtgHnp4FZ3trt%3DKBrbzRz1f8CEJ5MDobNA%40mail.gmail.com.

[Dick Fischbeck]

On Sun, Jan 8, 2023 at 3:24 PM Dx G <yipp...@gmail.com> wrote:

If you want to define flat faces, or a collection of angles, each face or angle would need 3 coordinates in space. Flat is 2d.

If you want to define a collection of lines or edges, each requires 2 coordinates in space.

If you want to define a collection of vertices only, each vertex is merely a single coordinate in space. But a point is not a structure, not a "building block."

However, if you want to define a collection of conical surfaces, these would be faces, each defined by the equation for that cone or section of a sphere. Again, it is hard to think outside the Descarte box. But that is exactly what Fuller was after.

[RC]

1. Domes constructed of panels attached edge to edge

2. Domes constructed from struts attached at their ends (usually with some form of hub)

3. ?

Third method that is simpler?  Please post a picture.  I am a visual guy.  Thanks.

[RC]

I suppose the simplest method would be an inflated balloon dome.

[Dick Fischbeck]

For example:

[Dick Fischbeck]

https://www.flickr.com/photos/8152259@N03/4770571517/in/dateposted-public/

[Dx G]

Yes, I'd be interested in #3 also.

Saying what something *isn't* does have some value, but the real pathway to development is discovering what the new thing *is*.

DxG

To view this discussion on the web visit https://groups.google.com/d/msgid/geodesichelp/a875a739-26ad-426a-bb80-e115ac71bf35n%40googlegroups.com.

[Dick Fischbeck]

#3 is described pretty well in the patent.  Just so you know, I've been trolling this structure for 20 years. Not to sell but to find interested people. Many nibbles, a few strikes.

https://patents.google.com/patent/US7389612B1/en

To view this discussion on the web visit https://groups.google.com/d/msgid/geodesichelp/CAF1iHD5%2BP2u_vXqcTnWGHGsfNYOsoYgx1v09T-TqUc1Z_0NhzA%40mail.gmail.com.

[RC]

Looking at the patent objectively, I would say it is really in essence a panel dome, but instead of the panels meeting on the edges, they overlap.  The overlapping has a water shedding benefit similar to shingling on a roof.  A similar design is that of the umbrella dome that creates a dome from hexagonal open umbrellas zippered together at their edges - also a panel dome.

[RC]

[Dx G]

For a price, one can buy at least one version of this.  I've seen a few companies come and go who sell them.   I think these folks are (where?) out of Alaska.  

https://intershelter.com/

One comment I heard from people who use them for hunting lodges. In a lot of places, they return to the lodge only to find that bears have trashed the building, no longer even useable.  However, there were claims that domes confuse the bears.  Hunters return to the lodge to find the ground around the base of the dome has worn to a trail. The bears go round and round, but don't seem to make an attempt to breach the structure, even though they could.  They go around looking for some thing to grab until they finally leave in frustration.  Quite an interesting behavioral issue if true.

DxG

[Ashok Mathur]

At one time the daughter of Monolithic dome founder was an active member of this list.

Monolith domes inflate a ballon and pour a concrete shell on it. When concrete is set, the ballon is deflated and reused.

See photos here

Sent from my iPhone

Ashok

On 09-Jan-2023, at 4:18 AM, Dick Fischbeck <dick.fi...@gmail.com> wrote:



To view this discussion on the web visit https://groups.google.com/d/msgid/geodesichelp/CAG0f9gQjPT_pqeqY7F-OZb5RjJgitqLZX3oEamDiuNXeUP9gSA%40mail.gmail.com.

[Ashok Mathur]

Correction.

They do not pour concrete. They spray it.

Ashok

Sent from my iPhone

On 09-Jan-2023, at 4:18 AM, Dick Fischbeck <dick.fi...@gmail.com> wrote:



To view this discussion on the web visit https://groups.google.com/d/msgid/geodesichelp/CAG0f9gQjPT_pqeqY7F-OZb5RjJgitqLZX3oEamDiuNXeUP9gSA%40mail.gmail.com.

[RC]

The inflated vinyl airform remains in place afterwards as a weather-proof coating.  After inflation, foam insulation is sprayed on the interior.  Then, rebar is attached with clips to the interior foam.  Concrete is sprayed onto that.  You get all of the concrete thermal mass on the interior where it belongs and the foam insulation on the exterior.

[Dick Fischbeck]

True. Craig Chamberlain's dome,  Now, Intershelter. I think Arco funded the project a few years back.

https://domevillage.us

https://www.design4disaster.org/2011/12/21/intershelter-brings-relief/

Here is Bruce Lebel's and Steve Elias's of World Shelters exhibition, also in Milan. 

https://www.designboom.com/architecture/world-shelters-u-dome/

[Dx G]

Interesting leads Dick.  That U dome is made from flat triangular panels.  I get the simplicity, and I'm sure its stronger than it looks, but I suspect if it took a good impact from a flying or falling object, it would poke in pretty bad.  That's why I'm on this jag for creased diamond panel domes. One of Fuller's patents actually showcases the use of a two-layer version that confers some "thickness" and stiffness to the panels that even work with paper or cardboard.  Same thing can be done with your randomes, where the flat ring of the dish can be connected to a mirror image dish facing the other way. Also confers some insulation value as well, given the air space in between.  I haven't seen this done much, but I suspect once the pieces are made, it would go up nicely and stand up better, even when the structure is challenged by projectiles, wind and snow load.  Paper models sure work, so hopefully it will scale up just fine, even if frequency needs to be increased for optimization.

DxG

[Dick Fischbeck]

You mention frequency. These are the equations for frequency of tetrahedral, octahedral and icosahedral spheres, in that order. n is the number of vertexes.

f=sqrt((n-2)/2), f=sqrt((n-2)/4) and f=sqrt((n-2)/10).

[RC]

Or, choose a frequency and find the number of vertices

tetrahedron:   vertices = 2 + 2(frequency^2)

octahedron:   vertices = 2 + 4(frequency^2)

icosahedron:  vertices = 2 + 10(frequency^2)

[Dx G]

Nice work guys. Now I won't need to do algebraic inversion.  Here's to the students of Euler :-)

DxG

[Dick Fischbeck]

Full disclosure, I agree with Fuller that nature cannot be using pi because there must be a discrete geometry in play in nature instead. 

I think a sphere has a finite number of vertexes. This is where I'm coming from.  

[Ashok Mathur]

One easy and plausible answer as to the number of vertex that a sphere has is zero.

Regards

Ashok 

Sent from my iPhone

On 11-Jan-2023, at 4:57 AM, Dick Fischbeck <dick.fi...@gmail.com> wrote:



--

--
You received this message because you are subscribed to the "Geodesic Help" Google Group
--
To unsubscribe from this group, send email to GeodesicHelp...@googlegroups.com
--
To post to this group, send email to geodes...@googlegroups.com
--
For more options, visit http://groups.google.com/group/geodesichelp?hl=en

---
You received this message because you are subscribed to the Google Groups "Geodesic Help Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email to geodesichelp...@googlegroups.com.

To view this discussion on the web visit https://groups.google.com/d/msgid/geodesichelp/CAG0f9gTNtdAdXxAK%3DYVNATQmwRHkz7gt_J1ocuo_Kg-du7Bo%3Dg%40mail.gmail.com.

[Dick Fischbeck]

Exactly what I am questioning. How can that be.

[Ashok Mathur]

By the traditional method of starting with small numbers and progressing up:

The smallest Structure in the space will have only four vertices.
An octahedron has six vertices. 

A cube has eight vertices.

And icosahedron has 12 vertices.

As the number of vertices increases, they will get closer to each other on a sphere of unit radius.

When it is increased to a very large number, the vertices will be indistinguishable from each other and hence can be counted as infinity or as zero.

Regards.

Ashok.

Sent from my iPhone

On 11-Jan-2023, at 7:18 AM, Dick Fischbeck <dick.fi...@gmail.com> wrote:



--
--
You received this message because you are subscribed to the "Geodesic Help" Google Group
--
To unsubscribe from this group, send email to GeodesicHelp...@googlegroups.com
--
To post to this group, send email to geodes...@googlegroups.com
--
For more options, visit http://groups.google.com/group/geodesichelp?hl=en

---
You received this message because you are subscribed to the Google Groups "Geodesic Help Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email to geodesichelp...@googlegroups.com.

To view this discussion on the web visit https://groups.google.com/d/msgid/geodesichelp/CAG0f9gRSA4kPQHZq64LjqiOzxGowSvYa61WpjXEgGXu6G3icrg%40mail.gmail.com.

[Dick Fischbeck]

But there are no continuums. 

[Bryan L]

On Wed, 11 Jan 2023, 12:48 Dick Fischbeck, <dick.fi...@gmail.com> wrote:

Exactly what I am questioning. How can that be.

Because a sphere is a mathematical concept.

--
--
You received this message because you are subscribed to the "Geodesic Help" Google Group
--
To unsubscribe from this group, send email to GeodesicHelp...@googlegroups.com
--
To post to this group, send email to geodes...@googlegroups.com
--
For more options, visit http://groups.google.com/group/geodesichelp?hl=en

---
You received this message because you are subscribed to the Google Groups "Geodesic Help Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email to geodesichelp...@googlegroups.com.

To view this discussion on the web visit https://groups.google.com/d/msgid/geodesichelp/CAG0f9gRSA4kPQHZq64LjqiOzxGowSvYa61WpjXEgGXu6G3icrg%40mail.gmail.com.