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RNDmodelshop — Octahedron and Cube 'Dual' (W-43)
Published: 2010-05-11 01:35:45 +0000 UTC; Views: 1994; Favourites: 19; Downloads: 24
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Description
2 polyhedron in one!This is a 'dual' of both an octahedron (stained dark) and a cube (clear coated). They are duals mathematically, because they relate to each other 'one to one' in the number of edges (12 each), and they relate as compliments to the number of planes to number of vertices (8 each).
This is one of the more difficult pieces to make, because each has 2 different lengths. In fact their exact relation to each other is the square root of 2, which is also the relationship of either of the 2 shorter sides of a 45' triangle to its hypotenuse. Each of the wood pieces is cut just halfway thru so they snug fit like Lincoln Logs. The 3 way compound miters on the cube are different than the 4 way compound miters on the octahedron.
...ol' Pythagoras told me all that in exchange for a cup of coffee and a prune danish once when he was kinda down on his luck...
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Comments: 14
I'm not sure I understand well what this is supposed to be (I'm a chemist but my knowledge of geometry is quite deficient) but I really like it. It looks stunning and I adore that it has two colours 
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thank you Mfmp I really like how the two colors set them apart so well, yet we can still see how they relate to each other
*cheers*
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Funny coincidence, I was playing yesterday with this combination while working an a 3D fractal mesh.
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that's very cool.
It still surprises me how often we find these geometric shapes can crossover so many different ways
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Thanks bear! Been a while!
Yah this model has been on DA for a while, just never got around to entering it into any groups, I guess I kept overlooking it somehow!
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I hate to admit how long ago this was but I use to build models like this out of colored paper.
I wish my wood working skill were better for I have log want to try to use Japanese joinery to build geodesic spheres and than come back and use them as frames to weave into. If I am right this would create a hyperbolic paraboloid or a hyperbolic vortex of woven mesh (depending on how the yarn was anchored) suspended inside the spheres. I just have never had the skill or tool to try it.
I do love you work and it has rekindled these old dreams.
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Thank you bear
I have seen a few CGI versions of what you mean around, and back in the 50s some were done in string or fishing line. I'd like to do one, but expansion / contraction over time may affext the string staying tight and that scares me!
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I know the type of tension construction you are talking about, I built a lot of those too. My most ambitious one was in school. I took thick walled pipe and wielded the ends closed. With lots of aircraft cable I built a 12 foot sphere out an amazing number of amazingly small pieces.
You my weavings I want to build a ridged frame like you are doing.
I did not like the ones I built with hubs because the hubs where ugly.
I have used fine wool and mohair for the one I built and that work well it last for about ten years before it was stolen out of the lobby of the place that bought it.
It is just I have always dreamed of doing a better job and have never figured out how to.
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yah thats always the trick and can be frustrating at times. I think I solve alot of these because of my original backround as an architectural modelmaker. Alot of improvising and problem solving under tight deadlines.
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