Two new noble polyhedra - a new source of convex hulls to search from?

For general discussion of polyhedra, not necessarily Stella-specific.
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Ulrich
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Re: Two new noble polyhedra - a new source of convex hulls to search from?

Post by Ulrich » Wed Dec 02, 2020 11:56 am

In the meantime I found one more pair. It is derived from an augmented dodecahedron:

Image

Image

senkoquartz
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Re: Two new noble polyhedra - a new source of convex hulls to search from?

Post by senkoquartz » Wed Dec 02, 2020 2:15 pm

Ulrich wrote:
Wed Dec 02, 2020 11:56 am
In the meantime I found one more pair. It is derived from an augmented dodecahedron:

Image

Image
Is that different from the pair in my OP post? I can't see any difference

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Ulrich
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Re: Two new noble polyhedra - a new source of convex hulls to search from?

Post by Ulrich » Wed Dec 02, 2020 3:40 pm

Oh, sorry, you're right, it's the same. I didn't look carefully.

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Re: Two new noble polyhedra - a new source of convex hulls to search from?

Post by senkoquartz » Fri Dec 04, 2020 5:17 am

Put together a very nice list of .stel files for the known nobles and special compounds (i.e. doubled-up facets and uniforms)
https://1drv.ms/u/s!AgVMslM5Ti8XlFQ-pc0 ... F?e=POEJXP

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Re: Two new noble polyhedra - a new source of convex hulls to search from?

Post by senkoquartz » Sun Jun 06, 2021 3:00 am

I'm trying to figure out a way to find 120-vertex noble polyhedra with stella.
Does anyone have any smart ideas?

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Ulrich
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Re: Two new noble polyhedra - a new source of convex hulls to search from?

Post by Ulrich » Mon Jun 07, 2021 10:22 am

I gave my computer another 16-GB memory and I got some noble 120-vertex-polyhedra but all of them were compounds. And in many other cases Stella crashes as before. I tried all uniform ones and their duals, the compounds of pairs of chiral 60-vertex noble polyhedra but I didn‘t find any distinct new one.

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Re: Two new noble polyhedra - a new source of convex hulls to search from?

Post by senkoquartz » Wed Sep 22, 2021 3:04 am

Ulrich wrote:
Mon Jun 07, 2021 10:22 am
I gave my computer another 16-GB memory and I got some noble 120-vertex-polyhedra but all of them were compounds. And in many other cases Stella crashes as before. I tried all uniform ones and their duals, the compounds of pairs of chiral 60-vertex noble polyhedra but I didn‘t find any distinct new one.
May I suggest the uniform compounds, and "gridoid1", "gridoid2", and "gridoid3" in my folder (the hulls of rhombic triacontahedron stellations)

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Re: Two new noble polyhedra - a new source of convex hulls to search from?

Post by senkoquartz » Thu Sep 23, 2021 9:00 pm

Ulrich wrote:
Mon Jun 07, 2021 10:22 am
I gave my computer another 16-GB memory and I got some noble 120-vertex-polyhedra but all of them were compounds. And in many other cases Stella crashes as before. I tried all uniform ones and their duals, the compounds of pairs of chiral 60-vertex noble polyhedra but I didn‘t find any distinct new one.
Also, the hulls of the duals in this folder - isohedra with equilateral triangles. In particular "du ditrigonal a", "dudid a", "dugid a", "dugid e", "dumid e", "Rhote a", "Rhote e", and "Unnamed".

https://onedrive.live.com/?id=172F4E395 ... 3953B24C05

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Re: Two new noble polyhedra - a new source of convex hulls to search from?

Post by senkoquartz » Mon Sep 27, 2021 6:56 pm

I have tried myself and not found anything. 5 sircos, 5 tics, and 10 tuts, and gridoid1 and gridoid2 still have to be searched.

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Re: Two new noble polyhedra - a new source of convex hulls to search from?

Post by robertw » Tue Sep 28, 2021 1:52 pm

Ulrich wrote:
Mon Jun 07, 2021 10:22 am
I gave my computer another 16-GB memory ... Stella crashes as before...
Stella is still a 32-bit program, so it has a limit of 3 GB of memory. So I'm afraid adding won't memory won't make a difference.

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Re: Two new noble polyhedra - a new source of convex hulls to search from?

Post by Ulrich » Wed Sep 29, 2021 8:35 am

Robert,
does this mean that we will never be able to solve the noble polyhedra problem with the help of Stella4D?

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Re: Two new noble polyhedra - a new source of convex hulls to search from?

Post by robertw » Wed Sep 29, 2021 3:51 pm

Ulrich wrote:
Wed Sep 29, 2021 8:35 am
Robert,
does this mean that we will never be able to solve the noble polyhedra problem with the help of Stella4D?
No, but it might be a while. I'll try to get it to compile for 64-bit again sometime, but I seem to remember it wasn't straight forward.

Another thing I should do is add the ability to search for nobles without having to actually generate all the faceting data. It really only needs to test each possible facet as it goes, not store all the possible facets too. The problem then would be time, and I'm not sure how long this would take. Depends how many combinations there are, but it's probably manageable.

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Re: Two new noble polyhedra - a new source of convex hulls to search from?

Post by Ulrich » Thu Sep 30, 2021 7:53 am

That would be great! I‘m really eager to create isohedral facetings from Grid.

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