What's the most complex model you've ever made?

Show us your models and discuss model-making techniques. Paper? Wood? Single vs double tabs? etc.
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marcelteun
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Re: What's the most complex model you've ever made?

Post by marcelteun » Mon Aug 17, 2020 9:15 am

I see that I promised to update this discussion with a model I built. It is this one:

Image

It doesn't consist of many faces, but it was hard to build. I failed once, many years ago. Then after some years I decided I should try again and then I thought more about how to solve the problem. I came up with a solution and then it was no problem at all and I finished it.

The polyhedron itself consists of regular heptagons only (each using one colour). That isn't really possible, of course, but I allowed them to be folded over diagonals according to a shell-fold and then it is possible. It is very hard to see the heptagons here, but here you can see an interactive 3D model:
http://tunnissen.eu/polyh/local_off.htm ... istance=18
(The link contains an link to an off-file that you could download and load in Stella if you prefer)

Once you understand how the heptagons are folded and connected, you "only" need to cut and paste regular heptagons. Chiral models can be hard to build, as everyone here probably knows, but this one was extra tight around the five-fold axes. Especially because I use cardboard that is quite thick (250 grams / m^2)

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Ulrich
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Re: What's the most complex model you've ever made?

Post by Ulrich » Sat Aug 22, 2020 11:27 am

Very nice model, cool and elegant colouring.
Is it so that in the polyhedron always one edge must be
counted twice because two edges of one heptagon meet
there?

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marcelteun
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Re: What's the most complex model you've ever made?

Post by marcelteun » Sun Aug 30, 2020 6:33 pm

Thanks, Ulrich!

You made a interesting observation! It is true that many models with folded regular heptagons that I made have that property: they consist of heptagons where two sides of one heptagon are glued together. I am not sure why that works well, but it might be related to the fact that you are left with something that has a pentagon base (though not flat either).

However there are also models that don't have this property, e.g. these ones:
http://tunnissen.eu/polyh/local_off.htm ... istance=13
http://tunnissen.eu/polyh/local_off.htm ... istance=13
http://tunnissen.eu/polyh/local_off.htm ... istance=18

But in the one I just built: yes, to see these are heptagons, you'll need to count one edge twice for each heptagon since two edges are glued together.

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