Put a polyhedron inside another

The place to talk about Stella4D, Great Stella, and Small Stella. Feel free to ask questions about them here.
Post Reply
Carabama
Posts: 4
Joined: Sun Jan 05, 2020 3:27 pm

Put a polyhedron inside another

Post by Carabama » Mon Jan 13, 2020 6:04 pm

Hello all,
so far I used Great Stella in a intuitive way but now I need to get images of precise polyhedron(s) inside another/others, for a lecture I am giving in France. For example I need to make appear an icosahedron inside and "kissing" so to speak a dodecahedron , a cube inside an icosahedron etc. I think I will keep it simple for this lecture and will need only those kind of images with the 5 platonician solids.
Is it possible to get these images with Great Stella ?
Thank you for your help !
Richard

User avatar
robertw
Site Admin
Posts: 529
Joined: Thu Jan 10, 2008 6:47 am
Location: Melbourne, Australia
Contact:

Re: Put a polyhedron inside another

Post by robertw » Wed Jan 15, 2020 2:31 am

Here is the general way to put one polyhedron inside another.
  • Start with one of the models
  • Decide how big you want it using one of the items on the Scale menu
    Image
  • Put it into a memory slot (keyboard shortcut: m1)
    Image
  • Load the second model
  • You might want to change the colour of the model now while it's separate
  • Again, set its size. The important part is setting the appropriate relative sizes between the two models.
  • Add the model from the memory slot

    Image
  • Now one model will be hidden inside the other. If you hide the outer faces, or some of them, you'll be able to see the model inside.

    Image
You can use Measurement Mode to help set the appropriate sizes:
Image

In this example however, you can do it all from the Scale menu.
  • For the icosahedron, set "Scale->Set Polyhedron Radius" to 10, say, before putting it in memory
  • For the dodecahedron, set "Scale->Set Polyhedron Inradius" to same value as before, ie 10, before adding the other model
Now the icosahedron will just touch the dodecahedron:
Image

Carabama
Posts: 4
Joined: Sun Jan 05, 2020 3:27 pm

Re: Put a polyhedron inside another

Post by Carabama » Wed Jan 15, 2020 4:52 pm

Thank you so much for your precise explanation, Rob.
I have 2 other questions : is there any way of moving a polyhedron relatively to the other ? Or for example, is there a way of making vertexes coincide ? The default combination makes centers of faces of one polyhedron coincide with vertexes of the other.

And is there a way of having transparent colors as in the model I send the picture of ? (in order to better see both polyhedron at the same time).
Was this image I found on the net made with your software ?

Kind Regards,
Richard
Image
Last edited by Carabama on Fri Jan 17, 2020 5:06 pm, edited 1 time in total.

User avatar
robertw
Site Admin
Posts: 529
Joined: Thu Jan 10, 2008 6:47 am
Location: Melbourne, Australia
Contact:

Re: Put a polyhedron inside another

Post by robertw » Thu Jan 16, 2020 10:35 am

No you can't easily move or rotate one part relative to the other. They've one model at this point. By default they are added with aligned symmetries. Try it with other combinations of polyhedra and you'll see that it usually has the orientation you'd want. You can't really align vertices between an icosahedron and dodecahedron because they just don't line up. At best you could only make a few coincide at once.

Sometimes there are clever ways to get models with different alignment, but not as easy and depends on what you want specifically.

Transparency is not officially supported, but it will be in the next major release, if I can ever get it finished! For now, you can do it by putting a texture on each face that has transparency.

Can't be sure, but that image doesn't look like it's from Stella.

Carabama
Posts: 4
Joined: Sun Jan 05, 2020 3:27 pm

Re: Put a polyhedron inside another

Post by Carabama » Thu Jan 16, 2020 5:06 pm

At best you could only make a few coincide at once.
Yes I am aware of that. But as the subject of the lecture relies on comparison of platonician solids relatively to the circumscribed COMMON sphere, I will need one way or another, to present these solids with aligned vertexes. I would prefer this rather than a compound without vertexes matching.

I only need to present the five solids with the common circumscribed sphere, 2 by 2 in the volume classification from the greatest (dodecahedron) to the smallest (tetrahedra). So : dodeca aligned with icosa, icosa aligned with cube, cube aligned with octa, and octa aligned with tetra.
This is basically what I need, and maybe in addition inscribed spheres, axis, etc, but I will see later. This is to present analogies in the structuration of a cell in biology and state of matter analysis (macromolecular, biological or colloidal, and sub-quantical/psychic).

I did not find a way of adding textures, I will look further.

Thank you

User avatar
robertw
Site Admin
Posts: 529
Joined: Thu Jan 10, 2008 6:47 am
Location: Melbourne, Australia
Contact:

Re: Put a polyhedron inside another

Post by robertw » Fri Jan 17, 2020 10:36 am

Bit confused by the common sphere thing. A circumsphere is one that passes through all the vertices, so if they shared a circumsphere, the polyhedra would not be inside each other, they would intersect with all their vertices on the same sphere. Maybe you mean a common centre, but equal edge lengths? Some would probably still intersect.

Either way, some combinations will work automatically, like dodecahedron and cube, dod and tet etc. The others are probably possible too, but not as easy. I should add a feature to rotate one part of a compound.

Textures is same as images. Use "Image->Load Image". However if you're using the opengl32.dll we talked about elsewhere, I don't think it supports textures at all, so you'd have to run without that to do this.

Carabama
Posts: 4
Joined: Sun Jan 05, 2020 3:27 pm

Re: Put a polyhedron inside another

Post by Carabama » Fri Jan 17, 2020 2:07 pm

Bit confused by the common sphere thing.
As the definition of regular polyhedra includes the rapport to the circumscribed sphere, I use this sphere in order to compare polyhedra. In my concept, despite the vertexes of an icosa pierce the faces of a dodeca (for polyhedra having circumbsribed spheres coinciding or of "same scale") one is inscribed or inside the other (reciprocally) because they share so to speak the same circumscribed sphere. If 2 polyhedra share their circumscribed spheres while having at least one vertex of a polyhedron coinciding with a vertex of the other polyhedron, it means they are aligned or "inscribed" in each other in my concept. In my approach the definition of inscription is not relative to vertexes of a polyhedon touching faces of the other.
I should add a feature to rotate one part of a compound.
That would be really a great addition !

I also notice the spheres we add in Great Stella have a pre-defined number of meridians and position of poles.
That would be great also to customize these parameters, having the possibility to set "spheres and meridians" options. For example placing the poles at the VERTEX of a polyhedron instead of aligned with center of an edge and not matching any vertex; or choose the number of meridians, including 0.

Is it already possible to achieve this with the current version ?

User avatar
robertw
Site Admin
Posts: 529
Joined: Thu Jan 10, 2008 6:47 am
Location: Melbourne, Australia
Contact:

Re: Put a polyhedron inside another

Post by robertw » Fri Jan 17, 2020 2:43 pm

The spheres that appear with "Display->Show Midsphere..." and "Display->Show Intersections with Spheres" are just intended as indicators, and no there's no way to alter their appearance.

You might want to try "Display->Show Reflection Planes" which also looks like a sphere, but made up of great circles in the planes of the reflection symmetries.

Post Reply