icosahedron construction

For general discussion of polyhedra, not necessarily Stella-specific.
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jacpot
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icosahedron construction

Post by jacpot » Mon Dec 04, 2023 4:55 pm

Hello everyone,
my questions are in the photo,
Sincerely
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robertw
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Re: icosahedron construction

Post by robertw » Tue Dec 05, 2023 2:18 am

It's not possible to make the yellow part in a single net, because the angle in the triangle at the corners that meet is 37.76 degrees, and there's 10 of them, so if folded flat it would cover 377.6 degrees, greater than 360 so they would overlap.

I've yet to try building a model where parts were only connected at points, so hopefully someone else can advise on that. I always thought it might be good to put some cotton across the joint, internally, to help keep them in place. Aside from that I think people just use a dab of glue, and sometimes a framework to sit the pieces in to hold them in place while gluing.

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jacpot
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Re: icosahedron construction

Post by jacpot » Tue Dec 05, 2023 7:37 am

agree for the 377.6 degrees,
but if we made one piece (which brings together four small pieces), plus one small piece, it would be easier to assemble under the main red piece, rather than five very small pieces, which accumulate the inaccuracies?

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robertw
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Re: icosahedron construction

Post by robertw » Tue Dec 05, 2023 12:27 pm

One reason for what it does is that the concave yellow fold is coincident with the concave red fold, and if you cut the yellow edges you can use their tabs to glue against the red faces for more internal support (but doesn't look like you'd need it in this model). You can disable this from the menu using "Nets->Coincident Edge Method->No Internal Support Required".

It still won't combine them though, as it tries to either maintain symmetry in the nets, or combine ALL symmetric parts into one. However if you reduce the symmetry to "No Symmetry" then it won't think about that (use the drop-down on the toolbar that starts by saying "Icosahedral"). First though, a couple of things: untick "Options->Recolor Sub-Symmetries" since you want to keep the colours, AND convert the stellation to be the new base model, using the left-and-down button in the top right corner of the Stellation View (otherwise changing the symmetry group will lose the choice of stellation cells).

The resulting nets are more messy, but it does combine 9 of the yellow triangles into one net, leaving one extra on its own. It splits up the red nets but you can use the original method for those. If you wanted to arrange the yellow triangles differently (eg 4 and 6 rather than 9 and 1) you could use cutting mode to force two cuts where you want them, and it should be able to combine the remaining ones.

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Ulrich
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Re: icosahedron construction

Post by Ulrich » Tue Dec 05, 2023 5:54 pm

I made some models with parts only connected at the vertices.I did that with a drop of „UHU hart“ which is a very quickly drying glue. I held each two pieces together and counted to 100, which was sufficient to keep them in place.

Ulrich

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