By all, that's wonderful. Why solve equations when you can jiggle about?

I also need a way to ... maybe even to generate Goldbergs with equal edge lengths as per the paper. I think that will require the solution of multiple simultaneous equations, there are no shortcuts for such arbitrary metric equalities in projective reciprocation. Can one even assume that all the ve...

Well Goldberg was interested in cages, and probably not interested in flat faces, because he was looking at molecular arrangements. I think these guys just realised, while doing the same thing, that they could expand this to say something interesting about polyhedra, as an aside to their molecular ...

Hi Robert, Yes, I think your remarks about the other types of equilateral polyhedron are spot on. I don't think I have yet found two equivalent definitions of a Goldberg polyhedron. One would have to go back and read Goldberg's original papers and see how rigorous he was - probably no more so than t...

C'est peut-etre une bulle appelé la Langue Anglaise?

Congratulations.

When can we see the 50-arm star with interior lighting?

Yes, you are right. I think "rectify" may be the operation of blending the polyhedron with its dual, I can't remember if that is the right word. It certainly gives a more accurate model (and nicer) than truncation. And yes it is augmentation not stellation. There might well be a convex core that can...

I estimate around 48 points, by: counting all the points in its outline, adding all the visible points within its outline, then assuming that the same number are hidden round the back. So it might well be the 50-point Moravian star - for hints on its construction, see for example http://en.wikipedia...

@3katie3. The centre of a triangle does look lopsided when seen from the side. One extremity of the triangle, say the left, will be a corner and a long way from the centre. The other extremity, say the right, will be an edge which passes much closer to the centre. When you spin the triangle about it...

Hi,

I cannot see the image of the star, it just shows a small box where the image should be.

Je l'aime.
C'est comme les dodecaèdres etoilés de M. C. Escher, mais avec plus de troux. Ou sont les lézards?

I like it.
It's like the stellated dodecahedra of M.C. Escher, but with more holes. Where are the lizards?

One interesting opportunity here comes from the fact that the faces come in parallel sets. On each side, one face from the small stellated dodecahedron is parallel to one from its great stellated cousin. Since these figures have opposite sides, also parallel, that makes four parallel faces in all. S...

Hi Peter, The backs lie in the 20 face planes of the icosahedron. These correspond to the 20 vertices of the dodecahedron, so matching them with the 12 pentagonal faces doesn't work. You could match the corners of each triangle to the 12 faces, which is of course the "same back and front" solution y...

C'est magnifique!

Looks really cool. Congratulations.