"Open-Faced" Polyhedra

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"Open-Faced" Polyhedra

Post by Nordehylop » Tue Feb 10, 2009 7:10 pm

A few months ago I designed and built two models of polyhedral stellations with sections cut away from their faces (so that only the true edges of the polyhedron would connect- actually only parts of the true edges). My blog posts on them can be found here:

http://proposition47.blogspot.com/2008/ ... odels.html

They are both fairly simple models, but look quite nice. I'm looking into building larger models of them out of wood and hanging them above my piano.

Has anyone else tried building something like this? I was inspired by the sculptor George Hart when designing mine , so I know I'm not the only one...
Also, does anyone have tips for designing these in Stella? I designed these two by subdividing faces and then faceting, but that's a pain. It would be nice if the vertices and edged of hidden faces were hidden as well , and if you could make models with infinitely thin faces. But that would perhaps be better mentioned in the "Feature Requests" section.
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Post by guy » Fri Feb 13, 2009 8:39 pm

I saw something along these lines at the Bridges Conference, London 2006. Sorry I can't remember who was giving the presentation, so not much help really.

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Post by robertw » Sun Feb 22, 2009 12:55 pm

Nice models. I'm afraid doing the first stellation of the icosahedron this way is not entirely original though. I made one which can be seen here:
But I don't think I was first either. Not that this detracts from your creation :)

Yes, subdividing faces and faceting is the way I do it. Generally I put the model in memory, then scale it down a little and add it back to itself (to get a compound of the model with itself at two slightly different sizes). Then subdivide and facet the same way on both components, also faceting lateral faces to connect the two. Bit of a pain, but I do it that way to maintain a solid model with two faces per edge. If you do it a different way I'd be interested to hear.

You might be interested in this tutorial too, which has some similar ideas.

And yes, it might be an idea to someday add the option to hide any vertices/edges where all surrounding faces are hidden.


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