Great Icosahedron - complex core

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kk6pr
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Great Icosahedron - complex core

Post by kk6pr » Mon Mar 18, 2013 4:46 am

I've made several Great Icosahedrons and have noticed that it isn't quite as stable as say a Great Dodecahedron. I'm using index cards or thick colored cardboard, but it still has a tendency to deform a little.

I thought of gluing a complex core inside to add some stability. For the Great Icosahedron, this appears to be a regular Icosahedron. However the complex core that Stella created was too small (even for making allowances for the interior tabs).

Is there a way to create a complex core of the correct dimensions? (I'm getting close by trial and error).

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Peter Kane
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Re: Great Icosahedron - complex core

Post by Peter Kane » Thu Mar 21, 2013 7:46 pm

kk6pr wrote:I've made several Great Icosahedrons and have noticed that it isn't quite as stable as say a Great Dodecahedron. I'm using index cards or thick colored cardboard, but it still has a tendency to deform a little.

I thought of gluing a complex core inside to add some stability. For the Great Icosahedron, this appears to be a regular Icosahedron. However the complex core that Stella created was too small (even for making allowances for the interior tabs).

Is there a way to create a complex core of the correct dimensions? (I'm getting close by trial and error).
Perhaps you could make 12 pentagrams and fit these onto the inside edge of each vertex section - just below the tabs. You should be able to measure the pentagram edge length accurately enough from one of the long triangles that make up the vertex piece. You could probably get away with a lot fewer than 12 of these.

PeteK

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robertw
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Post by robertw » Fri Mar 22, 2013 12:08 pm

I recommend doing it the same way I did, which is outlined here:

http://www.software3d.com/GreatIcos.php

You're right, the convex core (not "complex core" :)) is too small to be useful here. What you want is 12 5-triangle cups (like one cap from an icosahedron) to fit inside each part.

Image

kk6pr
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Post by kk6pr » Sun Mar 24, 2013 6:39 am

robertw wrote:I recommend doing it the same way I did, which is outlined here:

http://www.software3d.com/GreatIcos.php

You're right, the convex core (not "complex core" :)) is too small to be useful here. What you want is 12 5-triangle cups (like one cap from an icosahedron) to fit inside each part.

Image
Great - thanks, that looks like a better solution. Don't know where I got the complex....

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oxenholme
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Post by oxenholme » Tue Apr 02, 2013 12:12 pm

Ensure that you close any gaps at all 12 vertices and at all 20 re-entrant vertices.

The polyhedron should then be completely rigid and not need any internal reinforcement.

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robertw
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Post by robertw » Tue Apr 02, 2013 12:21 pm

Hmm, I can't say I agree with that. This model is a flexible mess without internal support in my experience! Maybe in theory it should be rigid, but in practice there's too much wiggle room at all those vertices. It's like an accordian!

But then I do like to make models as solid as a rock. I wouldn't even make a small stellated dodecahedron without internal support, unless it was very small.

I think internal support also makes it much easier to put the final pieces in. In fact I can't even imagine how it's possible without it.

Rob.

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oxenholme
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Post by oxenholme » Tue Apr 02, 2013 1:58 pm

There is a picture of mine on Facebook. It is completely rigid and very near perfect.

My Small Stellated Dodecahedron likewise has no internal reinforcement and is rigid.

You have to be VERY accurate, and very patient as you hold each vertex / re-entrant vertex until the cement sets and all hint of a gap has gone.

But that applies to pretty well every polyhedron!

I use 200 micron / 160 gsm card double tabbed and stuck together with balsa cement.

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