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Colouring Snubs

 
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Ulrich



Joined: 29 Jan 2008
Posts: 87
Location: Germany

PostPosted: Tue Oct 07, 2008 12:15 pm    Post subject: Colouring Snubs Reply with quote

Stella has some great features to do the colour arrangements for e.g. dodecahedral or icosahedral symmetries.
If you try to colour the snub triangles in a snub model in a regular way with only a few colours, (see:

.)

you have to do that by hand which can be rather painful. In this model 4 colours were used for the pentagons,
five for the icosahedral triangles, and another five colours for the snub triangles. It would be great if
Stella could support a feature to do this automatically. Robert what do you say, could you fulfil this desire? Rolling Eyes


Last edited by Ulrich on Fri Jan 14, 2011 11:02 pm; edited 1 time in total
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robertw
Site Admin


Joined: 10 Jan 2008
Posts: 394
Location: Melbourne, Australia

PostPosted: Thu Oct 16, 2008 10:22 am    Post subject: Reply with quote

The existing colouring modes are based on faces that lie in particular planes. Your idea is something new and it's not quite obvious what the general procedure would be for such an arrangement. Maybe just stick to colouring such models manually for now Confused

Rob.
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Ulrich



Joined: 29 Jan 2008
Posts: 87
Location: Germany

PostPosted: Thu Oct 16, 2008 7:52 pm    Post subject: Reply with quote

The snub colouring mode could be a small procedure of several steps.
In a first step you give colours to the dodecahedral and icosahedral
faces. In the second step, the faces adjacent to an icosahedral one
get the same colour like this one has. In a third step, the icosahedral
faces get new colours, different from the other ones. I think that this
isn't that hard to realize in the program. but it's hard to do by hand.

Ulrich
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Ulrich



Joined: 29 Jan 2008
Posts: 87
Location: Germany

PostPosted: Fri Jan 14, 2011 10:41 pm    Post subject: Reply with quote

This is how to colour a chiral polyhedron with intersecting faces, using only a few colours, where no two faces wearing the same colour, intersect. The 60 triangles of the W 114, the Inverted Snub Dodecadodecahedron can be arranged in pairs of two, sharing one common edge. The colours of these pairs can be arranged like those of a rhombic triacontahedron. Each pair of one colour is arranged like the faces of a cube:



Then all 60 triangles look like that:



The pentagrams and the pentagons are lying in planes parallel to those of a dodecahedron, so they can be coloured easily with stella's colouring tool.
The final model, using only 11 colours, looks like that:



Ulrich


Last edited by Ulrich on Mon Jan 31, 2011 2:33 pm; edited 1 time in total
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robertw
Site Admin


Joined: 10 Jan 2008
Posts: 394
Location: Melbourne, Australia

PostPosted: Sat Jan 15, 2011 4:08 am    Post subject: Reply with quote

I just thought of a partial answer for your original question.


  • Start with the snub dodecahedron.
  • Color -> Special Color Arrangements -> Icosahedral Arrangement 1
  • This colours the icosahedral faces, but leaves all the snub faces yellow.
  • Select a yellow face.
  • Color -> Take Color from Neighbouring Faces
  • When asked, answer "Outermost neighbouring faces".
  • Now the snub faces are also coloured in the icosahedral arrangement.


Your only problem then is that the icosahedral and snub faces match, so you then still need to manually change the colour of the icosahedral faces.
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Ulrich



Joined: 29 Jan 2008
Posts: 87
Location: Germany

PostPosted: Sun Jan 16, 2011 4:04 pm    Post subject: Reply with quote

Yes, this is exactly what I did, and even colouring only the 20 faces is a pain if you want to use just 5 colours. So I wished to have all this done automatically.

But when I proceeded to the nonconvex snub ones, I saw that things there are different and more complicated. So I'll be happy to do the colouring manually.

I found that it is helpful to add a second model, the symmetry of which matches that of the set of faces of the first polyhedron which you are going to colour.
The colours of this second one have to be preset in the desired way. Then you can transfer the colours to the faces of the first polyhedron, using the "add colour" tool.

When the work is done you just have to remove the second polyhedron again.

Ulrich
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oxenholme



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

PostPosted: Mon Jan 31, 2011 7:56 am    Post subject: Reply with quote

I made that snub many moons ago using plain white card.

Seeing the colour representations above has whet my appetite to having a go at making it in colour.

I would need six colours for the pentagrams and pentagons, another ten colours for the icosahedral triangles. Would I get away with the standard five colours for the snub triangles (as if they were a hexecontahedron), or would the intersecting faces prevent that from working?

I'm currently working on a polyhedron that I wish I hadn't started - it's only 65% complete yet it's already nigh on impossible to get anywhere near some of the tabs. It looked really good on Stella, in the flesh it's a tad disappointing.
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Ulrich



Joined: 29 Jan 2008
Posts: 87
Location: Germany

PostPosted: Mon Jan 31, 2011 1:38 pm    Post subject: Reply with quote

oxenholme wrote:
I would need six colours for the pentagrams and pentagons, another ten colours for the icosahedral triangles. Would I get away with the standard five colours for the snub triangles (as if they were a hexecontahedron), or would the intersecting faces prevent that from working?

Using the system described above, it works with six colours for the
pentagrams and pentagons and five colours for the snub triangles.
If you take the colour arrangement of a hexecontahedron, as you proposed,
you can avoid the pairs of adjacent triangles which I got using a triacontahedron:



There are no icosahedral triangles in this model (W 114).

Ulrich
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