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Nexorade Concept Illustrated by TaffGoch Nexorade Concept Illustrated by TaffGoch
Nexorade study animation • "Nexorade" is a relatively new term, and is preceded by "tensegrity," "rotegrity" and "reciprocal frame""Nexorade" was coined, and introduced, by Olivier Baverel, in the Nexus Network Journal, Vol.9, No.2, 2007, in his article entitled, "Nexorades Based on Regular Polyhedra" • Each "strut" element is called a "nexor" • This animation is based on a geodesic, class-I tessellation, frequency-3v polyhedron, and depicts nexor rotation, from 0-to-35 degrees, in 5° increments

Individual frames modeled in Google SketchUp • Animated in Photoshop and JASC Animation Shop 3

If you're interested in researching nexorades, you can read Baverel's PhD thesis paper, at:…

There are several more articles & documents available for download, at the Geodesic Help Group

( Note: Large animated GIF file • Give it time to load )
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bear48 Featured By Owner Jun 10, 2014  Professional
so very sweet
kbsztk Featured By Owner Jun 10, 2014
Hi Taff,

Can you please give me a brief description how to draw this in Sketchup?
Thank to you, I'm able to draw a dome or sphere, but once I rotate the strut (nexor) component they are not rotating the same way as yours. they are rotating towards outside and not intersecting with each other. I tried to rotate them by using the center point of the strut on the outside face, but it's not the right one. Can you tell me where is the rotating point or a brief description would be great as well.

Thank you in advance.

Your geodesic dome work is great and very helpful I learned a lot just watching your Sketchup models.
TaffGoch Featured By Owner Jun 10, 2014
I added a (hidden) centerline to the strut/nexor component, extending from the center of the sphere to the midpoint of the outer face of the strut. This centerline will be normal to the strut, when properly aligned/positioned.

The trick is to encapsulate the "strut" component within a "nexor" component. The strut component is the tube itself (which can have rectangular cross-section, as seen here, or circular/eliptical, whatever.) The nexor component includes the strut component and the sphere centerline. The geodesic sphere is built with nexor components (not strut components.)

Open a nexor component (I use a stand-alone "master" copy, located in its own layer, so it can be turned on/off. This master copy serves best when aligned straight up/down on the blue axis, left/right on the red axis, fore/back on the green axis.) Once the nexor component is open for editing, select/highlight the internal "strut" component and rotate it around the centerline. If you do this with similar components visible, you'll see that all the other (sphere) nexor components follow suit, with their internal struts rotating by the same angle.

That's it -- a component within a component. When you open/edit the outer-component, to rotate the inner-component, all of the outer-component copies "mimic" the inner-component rotation.

NOTE: For this particular model, I also "scaled" the strut (NOT the nexor) after each rotation, to simultaneously shorten ALL the struts by similar percentages. Otherwise, the struts overlap at the ends. (Sometimes, this is what you want, such as when building a reciprocal-frame.)

CAVEAT: Only if you have learned SketchUp well enough, will you understand the above description. Learning rotation around ANY axis is a prerequisite. Check out:…

SEE:… for screenshot of SketchUp display.
kbsztk Featured By Owner Jun 21, 2014

I was thinking that I started to understand these "struts, hedrons and nexor" things, but I think, I misunderstood something right at the beginning.
My new question is, how to create a "nexorade" sphere? What I did, is an icosahedron based one, but I realized, that yours is probably not. If you could give me a brief description of a nexorade based 1 or 2 v sphere (if it is doable) and from there I'm hopefully able to do higher frequencies if this method is working on all kind of classes and frequencies spheres at all?

My goal is to create dome models similar to yours with intersecting strait struts to try to build domes (without nails) of straight "regular" lumber by using half-lapped mortise and tenon. But I need the angles of the cuts. I wanna create models in different classes and frequencies for bigger structures as well. I'd also like to minimize the different strut lengths for easier construction if it's possible or as much as possible. Do you have any advice on what class and frequency would be a good choice to have the less different size of strut lengths? Class II icosahedron based spheres have less different strut lenghts than the same frequency in class I, but are they OK for this nexorade method?

Thanks in advance.
TaffGoch Featured By Owner Jun 21, 2014
You might be interested in this nexorade, which is a 2v, class-II icosa subdivision:…

... being similar to art by Rinus Roelofs, who has designed several nexorades sculptures:…
TaffGoch Featured By Owner Jun 21, 2014
Have you digested the papers by Baverel (his thesis, linked above) ?

Additional discussions and reference PDFs, at the Geodesic Help Group:!msg/…!topi…

3D SketchUp models:…

It took me several weeks, and much experimenting, to completely master the concepts and modeling techniques. I can not explain as well, or better, than do the above-referenced links.

(The depicted nexorade is, indeed, an icosahedron, 3v subdivision)
kbsztk Featured By Owner Jun 21, 2014
I will study your work and the links above.
Thank you very much for your help.
kbsztk Featured By Owner Jun 11, 2014

Thank you very much for your quick reply. Great detailed explanation. (I'm not a native English speaker.) It helps me a lot.
Those overlapping ends what you mentioned exactly what I need.

Rotation around any axis was learned from you previously as well.

Thanks again.
Gydrik2 Featured By Owner Sep 8, 2011
very cool, love your work :)
TaffGoch Featured By Owner May 20, 2011
The initial setup took some work, but by using SketchUp components, I could subsequently rotate one nexor, and all the others would rotate, equivalently. The animation frames were, therefore, fairly easy to produce.

Glad you liked it,
unigami Featured By Owner May 20, 2011  Hobbyist General Artist
Very interesting concept, and an excellent demonstration using SketchUp and and animation. It's interesting that the overall diameter of the sphere remains unchanged despite the movement of the struts. I bet this model a lot of work! Great job!
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Submitted on
May 19, 2011
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