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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