Added a LOC of polyhedra and other

[Sebelev]

https://polytope.miraheze.org/wiki/Level_of_complexity

Hello!
How do you like the idea of adding a level of complexity of polyhedron? Usually it is very difficult to calculate, especially for polyhedrons that are more complex than convex ones. It would be cool if Stella could calculate the LOC of any polyhedron herself, and this number would always be shown in the "polyhedron information" panel.

And my second idea is to improve the nets for the polyhedron, namely its tabs. By default, Stella creates double tabs for each polyhedron, and I liked this method. But what if a person wants to make a polyhedron with single tabs, which is made from nets that include only one outer piece of the polyhedron? In some cases this works, but in others the finished net is still created with the double tabs method, instead of single. This usually happens with convex polyhedrons that have only one type of element (for example: icosahedron), or partially with polyhedrons, for which this method would cause the tabs to bend inward. Can you fix this?

By the way, when will the new version of Stella be released? Maybe you already know the release dates?

[robertw]

(1) I wasn't familiar with LOC. Reading about it, I don't get it. It says it's 1 for Platonic solids, but how? LOC = value / halforder. For icosahedron, halforder = 60. How does value also = 60? It's not the number of external faces, or sum of faces, verts and edges. It's double the number of edges for some reason, but why?

It's a weird measure anyway. What's it for? If talking theoretically, intersecting faces don't make it more complex. That only really matters when you want to build a model. But in that case you don't care about symmetry. Building 60 of the same part still takes 60 times as long. So yeah, I need some explaining on this one.

Also, I'd only be able to do it in 3D. I don't have a way to count the external pieces in 4D.

(2) I don't follow this one either. You can select the single-tab method from the menu, and as far as I can tell it always works. And not sure what you mean about tabs bending inward. Can you send screenshots?



(3) I don't know when I'm releasing it yet. At the start of the year I was hoping it would be in the first half of the year, but here we are and I'm still not ready yet. Still things to do along with a bunch of boring admin-type stuff.

[Sebelev]

Yes, I'll try to explain it with pictures.

1. Actually, I don't understand how LOC is calculated . I just thought that LOC can be as useful as any other information about a polyhedron, because it is indicated under each uniform polyhedron in this Wikipedia. Let's think about how to calculate it correctly. And, of course, it will be almost impossible for 4D.

2. Yes, it works, but only with a single net that includes 20 triangles (for an icosahedron). But I wrote you about net that include only one triangle:

2.png (9.2 KiB) Viewed 12559 times

Which would take 20 pieces. It may seem to you that gluing 1 triangle is useless and complicates the work, but without this, some ribs are very easy to press in, because they are not glued with glue. And, with these scans, it will not be possible to make a polyhedron with the method of one tabs:

3.png (76.37 KiB) Viewed 12559 times

Most likely, Stella understands that a polyhedron consists of 1 type of faces (with icosahedral symmetry), and creates one type of net (triangle), which is actually logical. But in some cases it will be impossible to place tabs so that the polyhedron does not completely contain double tabs, so this is what happens. But it's strange that in the icosahedron and other deltahedra, tabs are created around the entire perimeter of the triangles.

For comparison: Triakistetrahedron. It’s situation is better, because most edges use the right method:

6.png (26.33 KiB) Viewed 12559 times

But still, double tabs are created on some edges:

…It is said that you cannot attach more than 3 images, so the continuation follows in the next message.

[Sebelev]

Yes, I'll try to explain it with pictures.

1. Actually, I don't understand how LOC is calculated . I just thought that LOC can be as useful as any other information about a polyhedron, because it is indicated under each uniform polyhedron in this Wikipedia. Let's think about how to calculate it correctly. And, of course, it will be almost impossible for 4D.

2. Yes, it works, but only with a single net that includes 20 triangles (for an icosahedron). But I wrote you about net that include only one triangle:

Which would take 20 pieces. It may seem to you that gluing 1 triangle is useless and complicates the work, but without this, some ribs are very easy to press in, because they are not glued with glue. And, with these scans, it will not be possible to make a polyhedron with the method of one tabs:

Most likely, Stella understands that a polyhedron consists of 1 type of faces (with icosahedral symmetry), and creates one type of net (triangle), which is actually logical. But in some cases it will be impossible to place tabs so that the polyhedron does not completely contain double tabs, so this is what happens. But it's strange that in the icosahedron and other deltahedra, tabs are created around the entire perimeter of the triangles.

For comparison: Triakistetrahedron. It’s situation is better, because most edges use the right method:

But still, double tabs are created on some edges:

…It is said that you cannot attach more than 3 images, so the continuation follows in the next message.

But still, double tabs are created on some edges:

8.png (7.52 KiB) Viewed 12556 times

Because one type of nets is created. Stella needs to learn how to make several identical types of nets with the same type of faces, because otherwise it will be impossible to make a polyhedron correctly. (For a triakistetrahedron: if you create a tab on the long side of an isosceles triangle, these edges will be glued by the double tabs method. And if you do not create a tab on this edge, it will be simply impossible to glue the polyhedron in these places).

Explanation of the phrase: “partially with polyhedrons, for which this method would cause the tabs to bend inward”: The fact is that with the correct placement of tabs in the Kepler-Poinsot solids in these places: (the photo shows a small stellated dodecahedron)

10.png (41.42 KiB) Viewed 12556 times

The tabs should be bent inward (that is, under the face as they should), but Stella creates double tabs:

11.png (11.34 KiB) Viewed 12556 times

I hope the explanation was clear. By the way, will the new version contain a lot of changes, or not?

[robertw]

Oh OK. Yes there are two cases where it will use double tabs even if the overall setting is for single tabs.

(1) If there are multiple nets of the same type, it will use the same tabs on each. So if two such nets meet at an edge of the same type, it will have to put a tab on both of them. The alternative is a different arrangement of tabs on each net of the same type, which could be confusing to put together. You'd need to be careful about which exact net glues to which net, even for nets of the same type. But if you really only want single tabs, you can drop the symmetry to No Symmetry, making every face a different type. Then there'll be no double tabs.

(2) For concave edges I don't think it's every a good idea to use a single tab. The tab would have to fold up rather than down and it's just harder to construct I think. If you really want you can select an edge in the net and set just that edge to the single tab method (probably after dropping the whole thing to No Symmetry). Is this something you personally want though, or more a hypothetical?