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 ...

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 ...

@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 ...

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 ...

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 ...

C'est magnifique!

Looks really cool. Congratulations.

Hi,

This is not an easy figure to construct. Some dimensions are arbitrary, but there are some determined relationships too.

I find the maths to be awkwardly developed. Personally, if I were working out coordinates I would use polar in the XY plane and Cartesian in the Z. And if you don't ...

OK, I have now read Gilson's book.

Sadly I can recommend it only to the most hardened polyhedron enthusiast (like me) ;) . Others will find it badly wanting.

Its approach purports to be based on symmetry, and to focus on polyhedra having a single major axis of symmetry, such as a regular prism. It ...

Thanks for the heads-up. I just ordered my copy before replying

@Kathy, Yes, I can see it fine - and if my clunky box can see it, most anybody can. Lovely model!

As a follow-up to my previous post, I am told that it does not have a regular "abstract" structure. In fact it is possibly the only known noble and self-dual polyhedron that is not regular in structure.

Its self-duality just made me realise that its abstract form appears to be regular, so we could write it as {5 5}

V-E+F = 24-60+24 = -12 so topologically it is a toroid of genus (2-(-12))/2 = 7
(where V = number of vertices, E = number of edges, F = number of faces).

I wonder if this regular ...

What kind of translator ignores ne ... pas ?

I don't use CNC either