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Great Icosahedron - complex core

 
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kk6pr



Joined: 09 Apr 2010
Posts: 6

PostPosted: Mon Mar 18, 2013 4:46 am    Post subject: Great Icosahedron - complex core Reply with quote

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



Joined: 25 Oct 2009
Posts: 79
Location: S.E England

PostPosted: Thu Mar 21, 2013 7:46 pm    Post subject: Re: Great Icosahedron - complex core Reply with quote

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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Joined: 10 Jan 2008
Posts: 395
Location: Melbourne, Australia

PostPosted: Fri Mar 22, 2013 12:08 pm    Post subject: Reply with quote

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" Smile) 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.

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kk6pr



Joined: 09 Apr 2010
Posts: 6

PostPosted: Sun Mar 24, 2013 6:39 am    Post subject: Reply with quote

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" Smile) 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.



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



Joined: 16 Jan 2008
Posts: 83
Location: North West England

PostPosted: Tue Apr 02, 2013 12:12 pm    Post subject: Reply with quote

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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Joined: 10 Jan 2008
Posts: 395
Location: Melbourne, Australia

PostPosted: Tue Apr 02, 2013 12:21 pm    Post subject: Reply with quote

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



Joined: 16 Jan 2008
Posts: 83
Location: North West England

PostPosted: Tue Apr 02, 2013 1:58 pm    Post subject: Reply with quote

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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