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?

## Colouring Snubs

### Colouring Snubs

Last edited by Ulrich on Fri Jan 14, 2011 11:02 pm, edited 1 time in total.

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

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

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.

- robertw
- Site Admin
**Posts:**401**Joined:**Thu Jan 10, 2008 6:47 am**Location:**Melbourne, Australia-
**Contact:**

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.

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

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.

Using the system described above, it works with six colours for theoxenholme 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?

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