C091210-cappells Tetrahelix build (Thanks Karl for the name)

C091210-cappells Tetrahelix build (Thanks Karl for the name)

Postby cappells » Fri Dec 11, 2009 5:36 am

(Post edited per Karl's reply below...thanks!)

This is a construct that I discovered on my own, and I have hardly ever seen in other builds. It is constructed entirely of tetrahedrons, hence the name.

This is a tetrahelix of length 3. Notice that the 3 "edges" are marked with white bars and each one is 3 bars long:
tetra_twist.jpg


Here are the build instructions:

1. Start with 3 tetrahedrons assembled as shown, using all the same color bars except for 3 bars of a different color as displayed here (in white):
tetra_twist_build.jpg

2. Add another white bar to the right of the white bar on top, and then complete the tetrahedron to the right.
3. Rotate the entire structure forward so that the white bar closest to you is now on top.
4. Repeat steps 2 and 3 as many times as you'd like. Every 3 tetrahedrons added will add another bar to each of the 3 strings of white bars.

Now for the challenge, which is more of a brainstorming session than a challenge. Using only tetrahelix segments of length 2 or more, what can you come up with as a complex build? Special consideration will be given to 1-axis or 3D symmetry, and no near-misses. Segments can be connected end to end or intersect each other, but no additional bars should be used to make the connections. To give an idea, here is the best I've been able to come up with (a miss, not following my own rules). Granted, I haven't spent much time on this since I created this, and I'm somewhat in a mental block:
geomag2a.jpg
Last edited by cappells on Sun Dec 13, 2009 11:59 pm, edited 1 time in total.
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Re: C091210-cappells Tetra-Twist (for lack of a better term)

Postby karlhorton » Sun Dec 13, 2009 8:19 pm

Curt,

chains of face-joined tetrahedra are fairly well known: but they are crap,
which is why no-one ever really uses them. They are weak,
and they have irrational angles between the
elements, which mean they never rejoin to themselves.

Your near misses are good: and be happy because there are no exact hits.

Buckminster Fuller called this pattern the "tetrahelix"

R. W. Gray has a nice paper on the tetrahelix (reproduction not permitted):

see http://www.rwgrayprojects.com/rbfnotes/helix/helix01.html

The late lamented Rafael Milan experimented with chains of tetrahedra -
he called his "tetrahedric curves" - here's his piece on them:

http://textodigital.com/P/GG/bp04c.php

And here's the only elegant Geomag construction he found:

tt3ccil.jpg


Karl
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Re: C091210-cappells Tetrahelix build (Thanks Karl for the name)

Postby cappells » Wed Feb 03, 2010 3:31 am

Being a bit "irrational" myself, I just can't let go of my fascination of the tetrahelix. It has become my "weak"ness. :)

So I played around a bit more...
tetrahelix2b.jpg
2-axis tetrahelix intersection


Somebody stop me!
tetrahelix3b.jpg
3-axis intersection!


I made a couple of other builds, but I got a little too greedy and the aforementioned weakness got the better of it before I could capture photos. I am still undeterred. I'm still convinced there is some way I can create a mobius strip out of this mess. :shock:
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Re: C091210-cappells Tetrahelix build (Thanks Karl for the n

Postby Eric » Sat Nov 28, 2020 9:15 pm

Hi cappells and everybody,

I understand so well what you feel (or 'felt' that would be much more accurate given the date of your post ;-)).
It is a shape I also (proudly :D ha ha!) came to by myself and it is sooooo! frustrating not being able to make something more of it.

As Rafael Milan wrote: "Promising as they seem, these curves have somewhat frustrating properties."
It is so true!

karlhorton wrote:The late lamented Rafael Milan experimented with chains of tetrahedra -
he called his "tetrahedric curves" - here's his piece on them:
http: //textodigital.com/P/GG/bp04c.php
This old link is dead. Here is a working one to Rafael Milan's page about his tetrahedric curves experiments, thanks to geomagmasters who host the site of the late Rafael Milan.

It is precisely with this shape that I asked myself questions about how to pick colors, their distribution in a pattern and what my artistic intention was with these choices.
I'll tell you about it later in another post.

In the meantime here is my tribute to this underloved shape ;)
DSC_8652_00001_01.jpg
So stylish at night!

20201127_184147.jpg
Color mess

20201127_184231.jpg
Light at the end of the tunnel


If members of the forum read these lines, please post a comment. It would be nice to know if there is someone around.

See you!
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Re: C091210-cappells Tetrahelix build (Thanks Karl for the n

Postby Peter Jepsen » Tue Dec 01, 2020 7:03 pm

I know I'm going off-topic, BUT.. a related side note if I may:

While building the tetrahelix, you sort of always 'twist right' or left, giving it the 'helix' shape.

If, however, you alternate between left and right, you will end up with this,
Which is a near-miss, credited to Adam Steele.
DSC_3242_idea_by_adam_steele.jpg


And playing around with that, I managed to come up with this:
DSC_3264_idea_by_adam_steele.jpg

And this:
DSC_3352_idea_by_adam_steele.jpg

This 'Sea anemone' for lack of a better description has a very satisfying internal structure, I urge anyone who hasn't tried it to give it a go.
(Eric, are you listening? :P )

EDIT: I see that Rafael also played with this structure, shown above. I don't know if he found it independently of Adam, I would not be surprised.
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Re: C091210-cappells Tetrahelix build (Thanks Karl for the n

Postby Eric » Tue Dec 01, 2020 10:03 pm

Of course I'm listening :D
Again good things to try. Thanks Peter. I will definitely try when I finish the homework you gave me ;-)

Maybe a coincidence, but the large ring reminds me of a shape I came up with last summer while trying to crisscross flying saucers (I call a flying saucer 2 opposing pentagonal pyramids ;-))
20201201_205923.jpg
Collision of two flying saucers

Chaining the 2-flying-saucers-crash shape I came across this heptagonal wreath.
20200826_015408.jpg
Strange colors I agree, but I made it at this time by scraping the bottom of the barrel ;-)
I don't remember if it's a near miss, which the photos would suggest or if all the rods connected well. Maybe the wreath was roughed up before I took the picture.

And if you take a close look at the outside edge of my heptagonal wreath, it looks like an inverted version of the inside edge of your large ring:
20200826_015611.jpg
Outer edge seen from the side

By the way, in this Christmas time, this heptagonal wreath with appropriate colors could make a nice decoration around a large Christmas candle :)
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Re: C091210-cappells Tetrahelix build (Thanks Karl for the n

Postby Peter Jepsen » Wed Dec 02, 2020 9:24 am

Those 2 collided flying saucers actually has a name that I know of..
I know that shape as an Oloid
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Re: C091210-cappells Tetrahelix build (Thanks Karl for the n

Postby Eric » Wed Dec 02, 2020 10:16 am

Thanks for the name even if it is far less poetic :lol: I didn't know it.
Last edited by Eric on Wed Dec 02, 2020 10:55 am, edited 1 time in total.
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Re: C091210-cappells Tetrahelix build (Thanks Karl for the n

Postby Eric » Wed Dec 02, 2020 10:54 am

I think the Oloid deserves its own topic in the "Math-related Geomag discussions" forum.
If you want to continue the discussion about it, please do it in this thread (nice vids and article inside)
or stay here for the tetrahelix shape ;-)
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Re: C091210-cappells Tetrahelix build (Thanks Karl for the n

Postby Eric » Sun Dec 06, 2020 11:13 pm

I made a crossover between Oloid ant tetrahelix :D

I also noticed that Galan Norman used the tetrahelix in these two original shapes : image 1 and image 2.

hope is not lost ;)
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