First I tried "Poly-> Put Models on Faces/Vertices", choosing the vertex option and applying to all, but you can't easily control orientation with this feature, and it ended up like this:

https://i.postimg.cc/VJvq5nz3/image.png

So I thought of another approach. First, set the edge length to 1 ...

Hi, sorry for not getting back to you. I probably just put it in the too hard basket and never got back to it. I probably figured it out bit by bit from websites and people here and there, but I don't know who or what to suggest now. It was years ago now. And I would have worked out a fair chunk on ...

Maybe post a screenshot here so I can see what you're seeing. Include the whole Stella window in case it tells me anything.

Works when I try it, but the 5-freq icosahedron has 750 edges, not 810. Ah, looks like you took the geodesic of the dual of the icosahedron, ie the dodecahedron, and used 3-freq, that has 810 edges. Still works for me though.

One reason for what it does is that the concave yellow fold is coincident with the concave red fold, and if you cut the yellow edges you can use their tabs to glue against the red faces for more internal support (but doesn't look like you'd need it in this model). You can disable this from the menu ...

It's not possible to make the yellow part in a single net, because the angle in the triangle at the corners that meet is 37.76 degrees, and there's 10 of them, so if folded flat it would cover 377.6 degrees, greater than 360 so they would overlap.

I've yet to try building a model where parts were ...

I don't know that there is a "correct" numbering system. The numbering was somewhat arbitrary in The 59 Icosahedra I think. Stella is able to find stellations of any polyhedron, so it has to proceed in a logical fashion, so it won't match The 59 Icosahedra. There would be more than one way to ...

For some uniform polyhedra, or stellations, you can see parts of a face from each side, so the back face colour would come into it then. Also as you say if you hide some faces or explode the faces apart.

I don't know what you mean about the cross-section view. Each face becomes a line in the cross ...

Back faces just refers to the back of the faces. So you can colour the back side of faces different from the front. There is no thickness to the faces, which is I think what you're after. You can display the dihedral angles between faces though, and the mitre angle which you would use to bevel edges ...

You can display the vertex figure in Stella4D. In this case it's an irregular tetrahedron. I wrote my own code to generate tetrahedra with any edge lengths which I used to create vertex figures like this. I'm not going to go into details about how I did anything specific in the code though.


https ...

The 3D vertex figures you mean? Some are simple and already available. Some I had to program in. And some I created with help/advice from others about what was required.

Yep I added all the models for Stella4D. The 4D library consists of the 3D vertex figures, from which Stella4D can generate the full 4D polytope.

Oh, sorry, thought you were asking about the construction of the truncated cuboctahedron, which seemed odd if you'd already managed the 120-cell!

Stella4D can construct it, but it doesn't do it based on reflection, so I don't know. I'll leave this for other to answer if they have any insights.

The topology is that of a truncated cuboctahedron, but it doesn't really work that way geometrically. If you truncate the cuboctahedron you'll get rectangles rather than squares. The result has to be adjusted to make all the faces regular. I'm not sure how you could construct it other than by ...

Well done, amazing job! Was this the one you said you hoped to finish in 2019?!