Non-Uniform 4D

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ndl
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Non-Uniform 4D

Post by ndl » Mon Dec 31, 2018 4:45 am

I just got Stella4D and I'm trying to play around with it. It seems you covered pretty extensively 4D uniforms, but I had trouble trying to create non-uniforms. I wanted to make an Icosahedral pyramid, for example, so I tried using a J2 pentagonal pyramid as vertex figure to create it, but it only gave me part of the polytope with no way to close it. Is there another way to create this? I found some 4D .off files online of various interesting CRF polytopes but I don't know how to create those on my own. Any suggestions? Thanks.

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Re: Non-Uniform 4D

Post by robertw » Mon Dec 31, 2018 8:44 am

Vertex figures only work for uniform polytopes, because it requires all vertices to be equivalent.

OFF files are in a simple text format, so you can look inside one and you'll be able to see how they work. But it's easiest to create them via code.

Stella4D has menu items to build a prism on the current polyhedron, but not a pyramid. I should probably add that, but I think I didn't because there's no obvious height to choose. Often it wouldn't be possible to keep the edges all the same length.

Building antiprisms would also be nice, but in 4D the top and bottom are duals of each other (actually they are in 3D too, but the dual of a regular polygon is the same regular polygon, rotated, so no one notices).

Actually the next major release will have a feature that would allow you to make an icosahedral prism, but this is still an unknown time away (unknown even to me!).

ndl
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Re: Non-Uniform 4D

Post by ndl » Tue Jan 01, 2019 4:24 am

What about an ability to cut off pieces of uniform polyhedra? That would give rise to lots of interesting non-uniforms. Maybe create it by choosing a cross section to cut it at (this could really be a great feature for 3D also!).

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Re: Non-Uniform 4D

Post by robertw » Tue Jan 01, 2019 7:09 am

Yeah maybe some day.

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Re: Non-Uniform 4D

Post by ndl » Thu Jan 17, 2019 4:17 am

I'm trying to work with .off files to create 4D non-uniforms, but it's way too tedious to try to figure out all the faces and cells that would connect the vertices. I found this program called qhull (www.qhull.org) that will calculate the convex hull and create an .off file from input vertices, but it only outputs the cell vertices, not the faces and not the cell by face like Stella4D requires. Do you have a program to enumerate the faces to create a file Stella can read? Thanks

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Re: Non-Uniform 4D

Post by robertw » Sat Jan 19, 2019 10:14 am

Just leave out the faces. Give the number of faces as zero and just list the vertices and cells.

Stella will guess the faces for you. For some polytopes this is ambiguous, which is why it allows you to specify, but usually it's not ambiguous so you can leave it out.

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Re: Non-Uniform 4D

Post by ndl » Sun Jan 20, 2019 3:50 am

It got confused when I listed cells, but I did a listing of just the vertices and it created the 4D convex hull for me! Thanks for your help.

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Re: Non-Uniform 4D

Post by robertw » Sun Jan 20, 2019 5:40 am

Oops, yep I got confused too, taking your lead :) It's the cells you don't need. You need the faces.

How to arrange faces into cells can be ambiguous, but you can leave cells out and let Stella guess.

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Re: Non-Uniform 4D

Post by robertw » Sun Jan 20, 2019 5:40 am

Oh, and if the model you're importing is convex, then you can get away with ONLY vertices, and Stella will create the convex hull of those vertices for you.

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Re: Non-Uniform 4D

Post by ndl » Mon Jan 21, 2019 3:39 am

Yes, convex hull is what I need and it works just fine. Thanks again

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Re: Non-Uniform 4D

Post by ndl » Thu Feb 07, 2019 2:57 pm

I made the following .off file but when I open it in stella4d and ask it to make convex hull the program crashes. Do you know what could be the problem?

cylindrical crind.off

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Re: Non-Uniform 4D

Post by ndl » Fri Feb 08, 2019 4:05 am

I figured out the problem: I was using the wrong formula to calculate the vertices so the ones I had were creating coplanar faces so that's probably why it was crashing. Once I fixed the formula it worked no problems.

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Re: Non-Uniform 4D

Post by robertw » Fri Feb 08, 2019 7:38 am

OK glad you figured it out. A warning rather than crashing would have been more helpful. I'll look into that.

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Re: Non-Uniform 4D

Post by ndl » Tue Feb 26, 2019 6:53 pm

I'm making .stel files of all the segmetochora, I was wondering if there is any way to embed in a file the ability to ask for a prism number and create something from that prism/antiprism like in the n-gonal prism built-in file. Thanks

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Re: Non-Uniform 4D

Post by robertw » Wed Feb 27, 2019 12:56 am

No sorry, you can't do that. The built-in ones that ask are not from files at all, they are built directly into the code and can handle asking for a parameter.

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