Temcor 12v domes

[TaffGoch]

 

While working on "Mexican" methodology for subdividing an icosahedron, I returned to the Antarctic dome design, for comparison. I recalled that Temcor employed a unique subdivision method, to reduce the number of unique dome components, whether panels or struts.

 

Temcor used/uses this subdivision method for their flat-panel and "v-beam" panel domes. The Antarctic dome and stadium domes, of 12v frequency, apparently all use the same chord factors. The subdivision method is likely proprietary, and hasn't been published. It's not "Mexican," nor any other "known" method, as far as I can tell.

 

The attached image is the "map" of the symmetry of the repeated chord factors, from diagrams of the Antarctic dome. As time permits, I'm planning to tackle a reverse-engineering of the chords. If anyone else knows of the method, it would save me the trouble of trying to reformulate the chords.

 

If you recognize the pattern, and can shed some light on the subject, it would be much appreciated. See what you can figure out from the "map."

 

Thanks,

Taff

[Richard Fischbeck]

Have you talked to Don Richter or Joe Clinton? I bet they would share the info.

[Hector Alfredo Hernández Hdez.]

Hi everybody!.

A few years ago, I did view a designs with rare configurations and with a low number of lengt struct different.., but dont keep with them..... :)

--
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

[Gerry in Quebec]

Taff’s question about the U.S. Antarctic dome piqued my curiosity. In
the article by Don Richter that Ashok referred to, there are two
diagrams. The plan diagram gives a dome floor diameter of 164 ft,
while the elevation diagram gives the dome height as 52 ft 7 in.
(52.5833 ft). As the dome is spherical, according to Richter’s text,
the latitude of the truncation plane must be 65.3409 degrees (or, in
terrestrial geography terms, 24.6591 degrees north latitude). And the
dome’s spherical radius must be 90.2283 ft.

But in a regular icosahedron the five vertices closest to the apex
have a latitude of 63.4349 degrees, not 65.3409 degrees. The
discrepancy of 1.9059 degrees suggests one of Richter’s dimensions may
be off. If we go by the floor diameter, then the dome height should be
50.6787 ft, not 52.5833 ft, and the spherical radius should be 91.6788
ft, not 90.2283 ft. But if we go by the stated dome height, the floor
diameter should be 170.1634 ft, not 164 ft, and the spherical radius
should be 95.1243 ft.

Another possibility is that Richter and company intentionally designed
the dome in such a way that the spherical geometry didn’t fully
conform to icosahedral symmetry despite the pentagon at the building’s
apex. Instead of the five parent spherical triangles being equilateral
with internal angles of 72, 72 and 72 degrees, as in a spherical
icosahedron, they would have been isosceles with internal angles of
72, 73.1365 and 73.1365 (a result of the unconventional 65.3409 degree
truncation latitude).

This explanation is consistent with the orientation of type-10
isosceles triangles, shown on Temcor’s colour-coded chart posted by
Taff. If the 65.3409 latitude value is correct, then the chord factor
for the repeating line of 12 green-&-white struts would be 0.0939,
giving a hub-to-hub length of 8.4714 ft. And for the 70 green-&-brown
horizontal struts circling dome, the chord factor would be 0.0815, for
a hub-to-hub length of 7.3578 feet. The dome’s total floor area would
be 21,096 sq. ft and the vertical height of the opening marked “Entry”
on Richter’s diagram would be 6 ft 10 - 5/8 in. (6.8858 ft).

All speculation of course. I’ll be interested to hear more on the
layout of this ‘ex-dome’.

Gerry

>  TemcorColorChart.jpg
> 543KViewDownload

[TaffGoch]

Gerry,

 

The Temcor 12v domes are, indeed, NOT icosahedral. They have 5-fold radial symmetry, but that's all. That's still true, with Temcor's current offerings, such as the Disney domes that flank the Epcot sphere. ("The Land" is one of them. I don't recall the other's name.)

 

I discovered this when I studied those same Antarctic diagrams, back when I created the Amundsen-Scott dome model, posted at the 3D Warehouse:

http://sketchup.google.com/3dwarehouse/details?mid=a43c84d44a145d0db418289a672426b3

 

What was, apparently, of more importance was that the "horizontal" struts be equal, and that they lay on a true arc. I got pretty close to the appearance of the dome, but haven't experimented enough with it, to develop the correct chord factors. The 12v Temcor domes look to have 14 chord factors, if the color map is correct. The panels share similar low-count variability. That would be a big advantage to a commercial operation like Temcor.

 

Temcor has also provided dome roofs that are based on the same panels, from the 12v dome, but with outermost rows omitted (1-or-more rows.) This is apparent from the "shallow" roofs, such as those depicted here:

http://sketchup.google.com/3dwarehouse/details?mid=d3d9ee74dbe4b6bb3e8e4c0d7f1fea28

 

Different profile domes, made from the same "off-the-shelf" v-beam panels.

 

-Taff

[TaffGoch]

Gerry,

 

By the way, I scaled the Amundson-Scott dome model to "full-size," and the diameter & height dimensions match the archived diagrams. The main corridor entrance is about 12.5 feet, which is the dimension I used to establish the geodesic arc that peaks at the opening's apex.

 

You can rely upon, and "measure," the macro dimensions of the model, but not the chord factors. They are only an approximation, at this time.

 

-Taff

[Gerry in Quebec]

Thanks, Taff. Yes, the 12.5 ft height of the entrance sounds right,
from the looks of one of the 1972-73 photos on the US Antarctic
Program website:

http://photolibrary.usap.gov/Portscripts/PortWeb.dll?query&field1=Filename&op1=matches&value=7273TOPASSEMBLY3.JPG&catalog=Antarctica&template=USAPgovMidThumbs

My earlier speculation was clearly based on an incorrect assumption
about the curve of the struts that arch over the entrance. I had taken
it to be a geodesic. But it can't be a geodesic because that gives an
entrance height of less than 7 ft, which is too short.
Gerry

>  Amundsen-Scott_PDF_render.png
> 199KViewDownload

[TaffGoch]

 

Quite right, Gerry. The strut arcs do not share the same centerpoint (and none of them share the sphere centerpoint.)

 

While an individual strut may have endpoints on the surface of a sphere (and are geodesic,) each arc-of-struts is NOT purely geodesic, by definition.

 

(I just now modified the warehouse model, to include the dome diagram. I had already included the station site plan, but forgot the dome plan/elevation.)

 

Reverse-engineering the chord factors is, therefore, not quite what we've been used to, for icosahedral geodesic subdivision methods. (That's what got my attention.)

 

-Taff

[TaffGoch]

 

Success!

 

I had another one of those late night revelations, while unsuccessfully trying to fall asleep. I had to get up, at 1:30am, to test the idea in SketchUp. After a few trial-and-error attempts, I was able to replicate the Temcor repetition and mirrored-symmetry of chord factors.

 

This subdivision produces nice arcs, crossing adjacent 1/5th-sections. Looks really smooth. The bottom-most rows of triangles, to truncate at ground level, are custom "stitched," and do not share the symmetry and mirroring of the modeled chord factors and triangular panels. (See attached photo.) This is as depicted in the color-coded diagram.

 

Temcor uses the same arrangement, without the lower ground rows of triangles, in their stadium roofs. Another photo is attached, showing the roof of the basketball stadium at Centenary College, Shreveport, LA (also 12v.) Of course, it uses the v-beam panels, but the symmetry & mirroring of the chord factors is identical.

 

I still have to produce a table of chord factors, color-coded to match the Antartica diagram. I'll post that, when done.

 

~Taff

[Gerry in Quebec]

Wonderful, Taff. So did you finally get some sleep after deciphering
the Temcor enigma?

I see the line of white struts that divides the first five rows of
triangles from the second five rows, counting from the ground up. But
what do you mean by 1/5th sections..... 1/5th of what?

Do you think there is a “method” underlying this type of spherical
tesselation, applicable to other frequencies. Or does it look like the
result of persistent iteration by Richter et al?
Gerry

>  Temcor experimental 02.png
> 469KViewDownload
>
>  Temcor experimental 01.png
> 239KViewDownload
>
>  Deconstruction 01.jpg
> 216KViewDownload
>
>  Centenary02.png
> 854KViewDownload

[Hector Alfredo Hernández Hdez.]

1/5 want to say over pentagonal piramid..

Let me check.
:)

[TaffGoch]

 

> "...what do you mean by 1/5th sections..... 1/5th of what?"

 

1/5th rotational-symmetry "pie sections," around the central vertical axis, or as Hector phrased it, pentagonal pyramid...

 

> "...does it look like the result of persistent iteration by Richter et al?"

 

Well, I didn't have to "iterate." I constructed this manually. The trial-and-error failures were guesses at the "latitude" of the "white" arc of chords. THAT I had to sneak-up on. Once that angle is established, all the rest is simple geometric construction.

 

After realizing the method, and producing the first few triangles, I got pretty quick at doing the rest. I've got one additional conjecture that I need to investigate, but then, I will produce a model that depicts the steps I used to size & position the isosceles-triangle faces. (Physically, it's a simple process. Mathematically, I wouldn't know how to describe it.)

 

~Taff

[TaffGoch]

 

Here's a nice surprise...

 

...regarding the Antarctic dome ~ an article from yesterday's "Ventura County Star":

http://www.vcstar.com/news/2010/nov/14/pieces-of-history/

 

Originally, only the top two rows of triangles were going to be shipped, and the rest left behind in crates. The initial plan didn't include moving all the parts, due to the costs of transportation. It looks as though someone came through with the funding.

 

Taff

[TaffGoch]

 

The Dutch "Aviodome" is/was a Temcor 12v aluminum dome. It's been dismantled, and is for sale:

http://architecturelab.net/11/buckminster-fuller-dome-for-sale/?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed:+architecturelab/news+(Architecture+Lab)

 

Even though the article states that Bucky was the builder, I suspect that Donald Richter's company, Temcor, Inc., was the entity involved.

 

An interesting YouTube video of its construction...

http://www.youtube.com/watch?v=gTibCwOn_4I

...which clearly depicts the Temcor parts.

 

Only 14 diamond panel configurations (chord factors) are required for this 12v dome. (The bottom-most row is composed of half-panels, of one of the 14, so there are actually 15 panels involved.) I've colored the last image to match the Temcor diagram colors (from the Antarctica dome.) The chord factors are the same for the Aviodome and the Antarctic dome.

 

-Taff

[TaffGoch]

 

A couple of more links, regarding the Aviodome, and its sale:

 

http://popupcity.net/2010/11/for-sale-buckminster-fuller-dome/

 

http://www.dome-te-koop.nl/fotos

 

(The sources for some of the photos I previously posted.)

 

-Taff

[Gerry in Quebec]

Are the chord factors now available somewhere?
Gerry in Quebec

On Nov 14, 8:21 pm, TaffGoch <taffg...@gmail.com> wrote:

> "Success!......I still have to produce a table of chord factors, color-coded to match the Antartica diagram. I'll post that, when done."

[TaffGoch]

Gerry,

 

Not yet. Since the Temcor dome is not based on an icosahedron, I question which chord factors would be of best use.

 

To "build" such a dome, you'd know the desired diameter of the footprint -- not knowing the circumscribing sphere diameter. While the sphere diameter, upon which normal chord factors are based, would give you the curvature of the roof, it has no real relationship to the footprint diameter.

 

I'm considering producing chord factors based on the footprint radius (of 1.000...) rather than sphere radius. What do you think?

 

(I could produce tables for both, of course.)

 

-Taff

[Gerry in Quebec]

Taff,

My preference would be chord factors referenced to the radius of the
sphere circumscribing the dome since that’s the most widely used
convention. There are exceptions, of course. Jeff Hill, who sells dome
plans on the Internet (www.domeplans.com), provides a set of chord-
factor-like numbers for calculating a dome’s dimensions. For instance,
to find the height of his 3/8ths, 3v icosa dome not counting the riser
wall, you multiple the dome’s floor diameter by 0.389679.

But as far as I know most dome builders use chord factors referenced
to the unit spherical radius even though for many designs the
spherical radius itself doesn’t show up in any of the final dimenions
needed for cutting & assembling the components.

In the case of the 12v Temcor Antarctic dome, the spherical radius
should be 90.228254 feet based on the dome height and footprint
diameter given in Don Richter’s two diagrams. At a spherical radius of
1 unit of length, the footprint diameter would be 1.817612 and the
dome height would be 0.582781.

Alternatively, if a floor diameter of 1 unit is used as the reference
dimension, the spherical radius will be 0.550172 and the dome height
will be 0.320630. The central angle of the chord between the dome’s
apex and any of the 70 vertices of the footprint should be 65.340871
degrees. Does SketchUp allow you to display/confirm that angle of
latitude?

I made a few half-hearted attempts to model the Temcor dome in Excel,
i.e., reproduce the various patterns of equal-chord pathways, but the
Solver feature wouldn't cooperate!

Gerry in Québec

[TaffGoch]

Gerry,

 

Here're the chord factors for a sphere of 1-unit radius.

 

Since I had to "sneek up" on the central angle of the footprint, based on photos and the diameter/height diagram, this is an approximation, but looks to be accurate to about 4 decimals. I provide 6 decimals, and these will produce a dome that is within 5/8" of the Antarctic dome (over a diameter of 164-feet, that's close enough for me, to stop trying to fine-tune it any further!)

 

I'm curious about how you would apply this information, since the height & footprint of the dome aren't (obviously) related to unit-radius chord factors. Dazzle me...

 

-Taff

[TaffGoch]

 

Here's the model (SketchUp 6), which contains 4 "scenes" (see attached images, below.)

 

-Taff

[TaffGoch]

 

Some relevent observations/characteristics:

[TaffGoch]

SketchUp model also posted at the Google 3D Warehouse:
http://sketchup.google.com/3dwarehouse/details?mid=9142431af448bd0c313cf1c2c0ee38cb

-Taff

[TaffGoch]

Gerry,

 

The "white" arc is of apparent importance, since that is the "foundation" upon which the other arcs are built/established.

 

I experimented with different declinations for the white arc. It doesn't appear to fall on a non-decimal angle, as I would have suspected. What angle would Richter have chosen? I assumed that it would be a whole number, since it can be arbitrarily chosen. The trial-and-error attempts I made were in this regard. I did not find a whole number (degrees) would produce the height/footprint of the Antarctic dome.

 

Last night, I had another potential relevation. What if he used radians? The model uses a white-arc estimated declination of 37.306° (by trial-and-error,) which is about 0.65 radians, so I tried that, today. I got a dome with a 164' diameter footprint, but with a height of 52', 5-5/16", so, it's close, but not spot-on.

I'm going to try one more decimal for the radians, 0.652, but that seems to be a rather odd starting place, as well. I'll see how close that gets me to the 52',7" height, reported on the diagram.

 

-Taff

[TaffGoch]

 

Well, the radians idea doesn't seem to pan out, either. Using 0.652 radians, I got a dome height of 52',7-7/8"

 

So, I'm still looking for the "secret" number/association for that white arc.

 

-Taff

[TaffGoch]

 

Okay, let's see if I can explain my method of building the subdivision, starting with the "white" arc.

 

Since I didn't know the declination angle, I started with half of the sphere arc, from the dome apex to the "corner" of the pentagonal footprint. I knew this to be too great of an angle, but I could get an idea of how much to reduce the angle by comparing the results to an "ideal" dome, as specified in the Antarctica diagram (and described by Gerry, in previous posts.)

 

Note that the topmost horizontal plane is NOT the ground plane, as it intersects the white plane. It's there just for the 72° reference.

[TaffGoch]

 

As Gerry previously noted, and as depicted in the Antarctic diagram of chords, the face triangles are isosceles.

 

This characteristic is used to find the first triangle that has a base on the white arc.

[TaffGoch]

 

The apex of the correct isosceles triangle is established by the intersecting line described by the intersection of two planes. A unit (1.0) line is drawn along this intersection.

[TaffGoch]

 

The endpoint of the newly-constructed unit-radius line is used to finish the first "white" arc triangle.

 

This triangle is copied, radially, to position the second "white" arc triangle. Connecting the apex of the first two triangles produces the base of the next row of triangles; i.e., the chord for the second arc (colored cyan, in the diagrams.)

[TaffGoch]

 

The first triangle-apex plane-intersection/construction method is repeated, to find the apex of the second triangle, now that we have the base line/chord.

[TaffGoch]

 

Repeating the initial triangle radial-copy process, on the second row triangle, locates and provides for the construction of the next arc baseline/chord.

[TaffGoch]

 

Process is repeated, to complete all rows/chords.

 

Once all chords have been produced, mirroring & rotating reproduces the rows "below" the white arc, to complete the 1/5th section of the dome. Only then can the footprint be measured.

 

My first trial produced the wrong footprint-to-height ratio, as I knew it would. By measuring how far off I was, I could adjust the "white arc" declination, and repeat the process. I had to do this, maybe, three times before I got the results in the posted model.

 

-Taff

[TaffGoch]

 

Doh! I should have seen this.

 

Producing the step graphics, and the animation, provided some insight. The temporary circular construction planes share the same rotation increments around the sphere centerpoint, as do the white arc chords. I could have constructed the full subdivision much faster if I had noted this before.

 

This also provides a potential method for describing the construction mathematically (although, I won't look into that, right now -- Gerry might?)

 

The subdivision method, essentially, relies on unit-length lines laying on the intersection-line between planes. I suspect this must be how Temcor designers produced the subdivision quickly.

 

-Taff

[Gerry in Quebec]

Taff,
Thanks for the images and chord factors. In Your SketchUp model, based
on the unit radius, the length of the chord from the dome apex to the
corner of the pentagonal footprint is 1.079321. I got this number
using the tape measure feature. The central angle of this chord, which
is also the latitude of the truncation plane of the Antarctic dome, is
65.32106 degrees ... namely 2 x arcsin (1.079321 / 2).

My own figures, based on Don Richter’s two dimensions in feet, are
1.079612 for the chord and 65.34087 degrees for the central angle. So
your and my numbers are pretty darn close.

However, when I calculate the central angles of the 12 chords along
that apex-to-footprint geodesic in your SketchUp model, and then add
all those angles together, I get 65.361499 degrees. The central angle
of the single chord between apex and footprint (65.321061) should
exactly equal the sum of those 12 central angles. But it doesn’t. The
difference – 0.040438 degrees – is significant and clearly internal to
SketchUp, i.e., it has nothing to do with the dome height and
footprint diameter we used as our starting points. Maybe this
discrepancy reflects the inherent accuracy limits of SketchUp?

You wrote: “I'm curious about how you would apply this information,

since the height &
footprint of the dome aren't (obviously) related to unit-radius chord

factors. Dazzle me... ”

I doubt I can dazzle you, but if I were to build this 12v dome or any
other spherical dome, at whatever scale, chord factors based on the
unit radius would allow me to easily calculate all kinds of
dimensions, both linear and angular: strut lengths, lengths and angles
of internal supports (e.g., backer studs), dihedral angles between
triangular panels and between panels and floor, axial angles of struts
for a hub-&-strut system, radial angles (angular distribution of
struts around hubs), triangle face angles, and compound angles for
cutting the ends of struts for a panelized dome.

Most or all of these dimensions can of course also be found using
chord factors referenced to the floor diameter. But I for one would
need to do a lot of extra number crunching because my various geodesic
calculators are all based on chord factors tied to the unit radius.

More later. Cheers,
Gerry in Québec

>  Temcor 12v chord factors.png
> 292KViewDownload

[TaffGoch]

Gerry wrote:

> ...chord factors based on the

> unit radius would allow me to easily calculate all kinds of
> dimensions, both linear and angular: strut lengths, lengths and angles
> of internal supports (e.g., backer studs), dihedral angles between
> triangular panels and between panels and floor, axial angles of struts
> for a hub-&-strut system, radial angles (angular distribution of
> struts around hubs), triangle face angles, and compound angles for
> cutting the ends of struts for a panelized dome.

True -- all, valid, important and required values, regarding
construction & component design. I reckon that it would be of help to
include a "footprint radius factor" and "height factor" -- added to
the table of chord factors.
______________________

I'll take a look at the summation of the 12 "longitude" chords. It's
possible that all the trial-and-error drawing/erasing, multiple times,
may have left behind detritus. I should probably start over with a
"clean sheet of paper," and produce a clean construction. I can then
compare the two to identify discrepencies.

-Taff

[TaffGoch]

 

All right then, I'm done.

 

Last night, I was thinking that the Temcor designers didn't start with footprint-diameter and height. They must have started with some underlying polyhedral form. This morning, I found it. (I now feel like an idiot.)

 

Temcor domes are founded upon the triacontahedron!

 

The Antarctic dome is not precisely 164' diameter, and not 52'7" height. There are fractional inches, rounded off. This makes sense. Why would they report to 1/32", for example.

 

Attached is the final assessment, with precise chord factors. The model includes a triacontahedron scene that depicts the association. I will be modifying the 3D Warehouse model, to incorporate these chord factors.

 

-Taff

[TaffGoch]

 

Here're the chord factors, to nine decimals.

 

-Taff

[Gerry in Quebec]

Congratulations, Taff!

Conclusion: If the Antarctic really was 164 ft in diameter, then it
was not 52 ft 7 in. tall after all. Rather, it was 52 ft 8-5/16 in.
tall!

A few hours ago I added up the central angles between the apex and the
white path of struts, based on your earlier chord factors. Result:
37.3170 degrees. I thought to myself, ‘Hmmmm, that angle looks rather
familiar.’ It’s very close to the latitude of one of the reference
points in the class II (triacon) breakdown, namely 37.3774. With your
new chord factors, the two values are now equal.

I guess I was totally stuck on the idea that Richter’s two dimensions
were exact.

- Gerry (also feeling like an idiot)

>  Temcor triacon.skp
> 170KViewDownload
>
>  Temcor triacon chord factors.png
> 190KViewDownload
>
>  Temcor triacon.png
> 118KViewDownload

[TaffGoch]

On Nov 24, 5:28 pm, Gerry wrote:
> - ... (also feeling like an idiot)

Well, hopefully we're not droolin' idiots...
_________________

I've updated the model at the 3D Warehouse, so that model will be the
reference standard for the Temcor tessellation:
http://sketchup.google.com/3dwarehouse/details?mid=9142431af448bd0c313cf1c2c0ee38cb

Readers should disregard any models previously-posted within this
thread. Use the 3D finalized 3D Warehouse model.

-Taff

[TaffGoch]

 

As an exercise to introduce readers to one of the newer capabilities of the newer Adobe Acrobat programs (and internet browser-helpers,) attached is a 3D PDF file of this dome, which can be viewed and manipulated.

 

Acrobat 3D files are unknown to most folks. You can rotate, zoom, change lighting and background, etc., without having to use SketchUp. SketchUp versions 7 & 8 support the free-trial plugin that will permit you to export 3D models to such PDF files:

 

http://www.simlab-soft.com/3d-plugins/3D-PDF-from-sketchup-main.aspx

 

-Taff

[TaffGoch]

 

Here's a preview of a solid render, "night lights" and black background.

[Gerry in Quebec]

Hi Taff,
Using spherical trig and successive approximation in Excel, I derived
the chord factors of the Temcor Antarctic dome.

My starting point was the latitude of the two end points of the path
of white edges, 37.377368140650 degrees . This is the central angle of
one of the two edges of a 2v full-triacon geodesic sphere. I then
found the remaining unknown spherical coordinates and chord factors
using Excel’s Solver tool, the step-by-step method you outlined a few
days ago, and Temcor’s colour-coded diagram showing the strut
positions.

As the Excel calculations were done independently of your SketchUp
chord factors, they serve as an independent check on your numbers, to
9 decimal places. Result: a perfect match. Here are the 14 chord
factors to 12 decimal places, from the dome apex down to the corner of
the pentagonal footprint.

0.078283756259
0.091957550333
0.084047898737
0.095152836494
0.089660678877
0.098086565294
0.094808430861
0.100603945721
0.099130528006
0.102547334421
0.102266116575
0.103777926749
0.103918298434
0.104199610634

By the way, it’s a 14 frequency, class II (full-triacon) icosa dome,
not 12 frequency. You may want to change the file name of the SketchUp
model in the 3D Warehouse.

- Gerry in Québec

On Nov 25, 12:17 am, TaffGoch <taffg...@gmail.com> wrote:
> On Nov 24, 5:28 pm, Gerry wrote:
>
> > - ... (also feeling like an idiot)
>
> Well, hopefully we're not droolin' idiots...
> _________________
>
> I've updated the model at the 3D Warehouse, so that model will be the

> reference standard for the Temcor tessellation:http://sketchup.google.com/3dwarehouse/details?mid=9142431af448bd0c31...

[Gerry in Quebec]

Taff,
In my earlier post I said I used Temcor's colour-coded diagram to
guide me during the Excel calculaitons. In fact I used your colour
coding. And now when I compare the two colour-coded diagrams, I see
the Temcor diagram includes a total of 50 equilateral triangles in the
dome, namely 10 clusters of five green-green-green no.5 triangles (or
is it just two colours that look alike?). Your strut arrangement, in
contrast, shows only isosceles triangles. Can you shed light on this?
Have you invented an alternative layout to Temcor's?

Maybe I've been staring at these triangles too long and am starting to
imagine things ;-)

Cheers,
Gerry

> > -Taff- Hide quoted text -
>
> - Show quoted text -

[TaffGoch]

Thanks Gerry, for the independent calculation verification.
 
Have you seen this subdivision method or results before? I've got to go through my referencea books, to see if it's been documented anywhere.
________________
 
On Fri, Nov 26, Gerry wrote:

>
> By the way, it’s a 14 frequency, class II (full-triacon) icosa dome,
> not 12 frequency.

Quite right. As far as I knew (at the time the file was named,) it was a 12v subdivision. It is obvious, now, that it is a 14v, but truncated at 12 "rows." I was considering describing this characteristic, on the model description page. I will change the file name, as well.

 

To the model, I've already added a dome "footprint" radius factor, and an "apex" factor, to the chord factors scene.
 ___________________
 
...at 2:24 PM, Gerry wrote:
>
> ...namely 10 clusters of five green-green-green no.5 triangles (or

> is it just two colours that look alike?). Your strut arrangement, in
> contrast, shows only isosceles triangles. Can you shed light on this?
> Have you invented an alternative layout to Temcor's?

The colors are, indeed, different. One's dark green, and the other dark cyan. I, too, had to do a double-take. In fact, I used a color-analyzer tool to discern the differences. In the model, I used a lighter color scheme, expressly for this reason. Hopefully, my colors are disparate enough, for even color-blind users.

 

So, no new layout -- It's Richter's, and the triangles are all isosceles.

 

-Taff

[TaffGoch]

 

Okay, I've revised the model description at the 3D Warehouse.

 

I'd appreciate anyone's critique. The description there, and the discussion here, should provide everything anyone would need to reproduce/design/construct a Temcor-style dome. (That's my objective, anyway.)

 

http://sketchup.google.com/3dwarehouse/details?mid=9142431af448bd0c313cf1c2c0ee38cb

 

-Taff

[Gerry in Quebec]

Taff,
You asked:

> "Have you seen this subdivision method or results before? I've got to go
> through my referencea books, to see if it's been documented anywhere."

For the moment, all I know is that it isn't Class II, Method 1. That
method results in something like 44 discrete strut lengths if CADRE
Geo has it right. As I recall, both CADRE Geo and Rick Bono's Windome
program both use method 1 for their class II calculations.

For the class II domes, Domebook II uses method 3 and refers to it as
the "triacon" method. It gives chord factors for frequencies 2, 4, 6
and 8.

Hugh Kenner, in "Geodesic Math and How to Use It", includes both
method 1 and method 3 in his discussion. For both he gives spherical
coordinates. In the case of method 1, the coordinates are for
frequencies 2, 4, 6, 8 & 12 but not 14. For method 3, he gives both
spherical coordinates and chord factors for frequencies 4, 6, 8, 12
and 16. Neither 10v nor 14v seem very popular!

From Kenner's data on class II, method 3, it should be pretty easy to
determine whether the Temcor dome uses method 3 or not.... just need
to give it a closer look. The Temcor layout, like method 3 (and the
Mexican method), has the advantage of a small number of chord factors,
where n = frequency, namely 14.

Cheers,Gerry in Québec
(where we've just had freezing rain, slightly alleviated by a cm of
snow)

[Gerry in Quebec]

I took a look at the class II, method 3 geometry in Dome Book 2 and
Hugh Kenner’s Geodesic Math book to see if it could possibly be the
basis of Temcor’s 14v Antarctic dome. It isn’t. Method 3, credited to
Duncan Stuart, doesn’t produce the orderly sets of side-by-side
isosceles triangles seen in the Temcor design.

By the way, Joe Clinton’s chord factors for class II, method 3 in Dome
Book 2 don’t all agree with Kenner’s.

Gerry in Québec

[Richard Fischbeck]

Once, someone pulled Joe's calculations out of the garbage and published them. True story.

--

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

[TaffGoch]

 

I believe it! Geodesic subdivision seems to have been a "dark arts" secret, for so many years. Just another reason I appreciate the internet, these days.

 

Still, it can be hard for a novice to get started. Thanks to everyone's help, here, I hope that we're satisfying a previously-unfulfilled need.

 

-Taff

__________________________

[Gerry in Quebec]

I wonder if the thief knew illegal dissemination of trig waste in the
Delta quadrant leads to theta radiation poisoning.

On Nov 27, 4:15 pm, Richard Fischbeck <dick.fischb...@gmail.com>
wrote:

> Once, someone pulled Joe's calculations out of the garbage and published
> them. True story.
>

> > GeodesicHelp...@googlegroups.com<GeodesicHelp%2Bunsubscribe@google­groups.com>

> >  --
> > To post to this group, send email to geodes...@googlegroups.com
> >  --

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

[TaffGoch]

 

An obscure Star Trek reference, if there ever was one...

[TaffGoch]

 

For readers who don't have, or don't want to use, SketchUp, attached is a 3D PDF file, which can be viewed & manipulated with the Adobe Acrobat reader.

 

The 3D depiction can be rotated, zoomed, etc., to examine the geometric basis of the Temcor subdivision method. Note that the primary-principal-triangle (PPT) is a triangular face of a Class-II, 2v subdivision of the icosahedron (aka, 2v triacon,) employing a unit radius for the circumscribing sphere.

 

Making the construction method a PDF file should make the process available to a wider audience, and make sharing the method easier, by using a more-universal file format.

 

-Taff

[Blair Wolfram]

Yes, it's called Domebook 2. After the wrong numbers were discovered, he fought to have the correct numbers published, and the revised chord factors in the 1974 printing are mostly correct.

 

Blair

On Sat, Nov 27, 2010 at 3:15 PM, Richard Fischbeck <dick.fi...@gmail.com> wrote:

[Gerry in Quebec]

Blair,
The Domebook 2 numbers I was comparing with Kenner's come from my
dogeared hard copy of the second printing (August 1971). Ironically,
the previous owner was a guy named Jim Strutt, from the area where I
grew up!

Taff,
Is the e-version of Domebook 2 legal, in the sense of respecting
copyright? I'm referring to the following link in the "sticky" item
found in GeodesicHelp's initial list of discussion topics:

http://www.publiccollectors.org/CompletePublications.htm

Looks like piracy to me.

Gerry

On Nov 28, 6:24 pm, Blair Wolfram <thedome...@gmail.com> wrote:
> Yes, it's called Domebook 2. After the wrong numbers were discovered, he
> fought to have the correct numbers published, and the revised chord
> factors in the 1974 printing are mostly correct.
>
> Blair
>

> On Sat, Nov 27, 2010 at 3:15 PM, Richard Fischbeck <dick.fischb...@gmail.com

>
>
>
> > wrote:
> > Once, someone pulled Joe's calculations out of the garbage and published
> > them. True story.
>

> >> GeodesicHelp...@googlegroups.com<GeodesicHelp%2Bunsubscribe@google­groups.com>

> >>  --
> >> To post to this group, send email to geodes...@googlegroups.com
> >>  --

> >> For more options, visithttp://groups.google.com/group/geodesichelp?hl=en

>
> > --
> > 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<GeodesicHelp%2Bunsubscribe@google­groups.com>

> > --
> > To post to this group, send email to geodes...@googlegroups.com
> > --

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

[TaffGoch]

 

On Sun, Nov 28, 2010 at 6:40 PM, Gerry wrote:
>
> Is the e-version of Domebook 2 legal, in the sense of respecting
> copyright? I'm referring to the following link in the "sticky" item
> found in GeodesicHelp's initial list of discussion topics:
>
> http://www.publiccollectors.org/CompletePublications.htm
>
> Looks like piracy to me.

__________________________________

 

Gerry,

 

I thought the same thing. I checked Shelter Publications website, and DB2 is no longer in print, although "Shelter" (the subsequent book, containing "Domebook 3") is in print, and for sale.

 

I checked this, before posting the DB2 link, in 2008.

 

I can't believe that Shelter Pub doesn't know that DB2 is online (in at least 3 places.) The Public Collectors website makes the offer to remove any posted book, if the copyright holder contacts them. Apparently, Shelter Pub hasn't done so. As long as they don't complain, it looks like they're okay with DB2 being in the public domain. (Perhaps, it drives more customers to Shelter Pub's current offerings.)

 

I downloaded a PDF copy, even though I already have a hardcopy. Get it while you can, folks.

 

-Taff

[Gerry in Quebec]

Taff;
You mentioned that the Public Collectors website offers "to remove any
posted book, if the copyright holder contacts them." Sounds like
burglars leaving a note on the victim's kitchen table: "Thanks for all
the free goodies. Please contact us if you object to being robbed.
We're in the Yellow Pages." Shouldn't the onus be the other way
round?
Gerry

[TaffGoch]

 

SketchUp model overlaid on Google Earth image of A.E.Wood coliseum, at Mississippi College, Clinton, MS. (Model oriented, to mimic both the camera perspective and sun shadows.)

Based on the scale in the lower left corner, this dome has a ~200-foot diameter footprint.

 

-Taff

[TaffGoch]

For comparison, at Google Maps:

http://maps.google.com/maps?hl=en&ie=UTF8&ll=32.335168,-90.332226&spn=0.000961,0.002559&t=k&z=20

-Taff

[Dick Fischbeck]

And I was hoping we could move on to method 5! There must be many more ways to distribute vertexes in a polyhedron. I'm not saying I know what those ways are.

On Sat, Oct 22, 2011 at 3:02 PM, TaffGoch <taff...@gmail.com> wrote:

To provide definitive closure on this discussion,...

...the Temcor subdivision method is "Method 4," as described by Joe Clinton, by Hugh Kenner, and in Domebook 2.

-Taff

[TaffGoch]

Hey, Dick,

This exploration took almost a year, just to realize the association! :)

It's too bad that the internet wasn't around, when Ducan Stuart developed methods 3 and 4. I suspect that questions would have been resolved in short order.

I reckon that you could look at Hector's "Mexican" method as Method-5....

-Taff

[Dick Fischbeck]

Barring objections from Blair, why are we so focused on placing vertexes on the surface of a hypothetical sphere? Steve Miller threw out that restriction recently with his latest sheds, what ever he calls the structures.

Plus, if we use Joe Clinton's conjectures, I am pretty sure the duals of his Goldberg polyhedrons will open up new doors to flexibility in structuring triangulated surfaces.

[Gerry in Quebec]

Hi Taff,
Do you know the page number for Kenner's description of Method 4?
I assume you're talking about Geodesic Math. I flipped through it but
didn't find the reference.
Thanks,
- Gerry

[TaffGoch]

Gerry,

Joe Clinton describes Method-3, in NASA CR-1734 - Polyhedral Subdivision Concepts, but labels it as Method-6. His Method-7 is what Domebook 2 calls Method-4.

Domebook2 describes Method-4 in one sentence, identifying the difference from Method-3.

Kenner only describes Method-3, neglecting to mention Method-4.

What I have described as Method-4, in previous posts, apparently differs from Domebook 2 and Clinton. Both references describe the equal-angular subdivision of the hypotenuse. I, instead, described it as an equal-angular subdivision of the short leg of the right-triangle, which produces the same chord factors that I got when modeling the Temcor/Richter method. So, I suppose, the Temcor method is NOT Method-4, but strongly related (and, apparently, not documented anywhere -- which astounds me, since the related methods 3 & 4 are documented.)

I, now, have to go back and try subdividing the hypotenuse, to get a (documented) "Method-4" result.

-Taff

[Gerry in Quebec]

Taff: It all makes sense now when I look at the one-sixth subtriangle
of the original icosa face.

I did all the trig for the 6v Temcor layout and described each step
(something like 35 in all) in words. Except for its value as an
example of how to apply spherical trig, it was pretty darn tedious and
maybe a waste of time because the coordinates and chord factors can be
found so quickly using Excel's Solver feature. And even that isn't
nearly as powerful as a SketchUp model.

Thanks for the explanation about the various methods. Good luck with
method 4 and the hypoteneuse.
- Gerry

[TaffGoch]

Here's a visual; depicting my retraction:

[Dondalah Proust]

Gerry,

You did such a fabulous job de-mystifying Method 3, any effort that you put toward de-mystifying Method 4 and Temcor is invaluable despite the effort that it takes.  You are the only one who has made sense, real sense, of Method 3.  Keep it up, please.  I, for one, look forward to seeing what you have for Method 4 and Temcor.

Taff,  is there any way you can make Joe Clinton's writings available in this group by snipping it, or by whatever means possible?  Thanks.

Dondalah

---

From: Gerry in Quebec <toomey...@gmail.com>
To: Geodesic Help Group <geodes...@googlegroups.com>
Sent: Monday, October 24, 2011 3:11 PM
Subject: Re: Temcor 12v domes

--
You received this message because you are subscribed to the "Geodesic Help" Google Group
--

To unsubscribe from this group, send email to GeodesicHelp+unsub...@googlegroups.com