Search found 95 matches
- Fri Jul 11, 2025 3:34 pm
- Forum: Polyhedra
- Topic: Millers rules (again)
- Replies: 6
- Views: 120
Re: Millers rules (again)
When in a cell diagram there are two independent pairs of enantiomorphous cells (so any combination can be added)
There are 9 combinations to consider.
So for example we have an polyhedron B and we have the cells c1L, c1R, c2Land c2R (and maybe other c cells) that could be added we should ...
- Wed Jul 09, 2025 9:00 pm
- Forum: Polyhedra
- Topic: Edge-Transitive Polyhedra
- Replies: 13
- Views: 89826
Re: Edge-Transitive Polyhedra
Abstractly, all isotoxal polyhedra come in dual pairs (some identical).
Most people assume a polar reciprocity about a concentric sphere in order to construct the dual. However the construction is not rigorous in Euclidean space. It is rigorous in projective space, and applying a homogeneous metric ...
Most people assume a polar reciprocity about a concentric sphere in order to construct the dual. However the construction is not rigorous in Euclidean space. It is rigorous in projective space, and applying a homogeneous metric ...
- Wed Jul 09, 2025 8:52 pm
- Forum: Polyhedra
- Topic: Is astro logix still trading?
- Replies: 3
- Views: 81
Re: Is astro logix still trading?
Astro Logix have a Facebook page, but their last post was over five years ago.
You could try sending them a message on Facebook, but I wouldn't hold out much hope.
https://www.facebook.com/astrologix/
You could try sending them a message on Facebook, but I wouldn't hold out much hope.
https://www.facebook.com/astrologix/
- Wed Jul 09, 2025 8:41 pm
- Forum: Polyhedra
- Topic: Millers rules (again)
- Replies: 6
- Views: 120
Re: Millers rules (again)
Rule (v) remarks that "But we allow the combination of an enantiomorphous pair having no common part (which actually occurs in just one case)". Any interpretation which allows more than one such solution to the full set is therefore wrong.
There are 12 cell sets (distinguishing enantiomorphs), so 2 ...
There are 12 cell sets (distinguishing enantiomorphs), so 2 ...
- Mon Jun 23, 2025 10:09 pm
- Forum: Polyhedra
- Topic: Edge-Transitive Polyhedra
- Replies: 13
- Views: 89826
Re: Edge-Transitive Polyhedra
Thank you. Remarkable stuff. Have you tried submitting your paper to a peer-reviewed publication?
You remark that "there are several dual pairs among them". Surely, the standard dual of an isotoxal figure will also be isotoxal. Thus, they must all either exist as a member of a dual pair, or be self ...
You remark that "there are several dual pairs among them". Surely, the standard dual of an isotoxal figure will also be isotoxal. Thus, they must all either exist as a member of a dual pair, or be self ...
- Mon Jun 23, 2025 9:21 pm
- Forum: Stella Forum
- Topic: Running on Wine
- Replies: 9
- Views: 36415
Re: Running on Wine
Is Wine any easier to set up than it used to be? I could never get past the default display settings, if it ever worked at all.
- Wed Dec 18, 2024 6:27 pm
- Forum: Polyhedra
- Topic: Current researches
- Replies: 0
- Views: 133520
Current researches
A forum for discussing current researches into polyhedra seems sorely lacking these days. So I thought I'd see if one here gathers any interest.
Several people are working actively on abstract polytope theory, in which the abstraction is a set-theoretic construct which captures the connectivity or ...
Several people are working actively on abstract polytope theory, in which the abstraction is a set-theoretic construct which captures the connectivity or ...
- Tue Dec 17, 2024 6:32 pm
- Forum: Polyhedra
- Topic: the 59 stellations of the icosahedron
- Replies: 3
- Views: 38909
Re: the 59 stellations of the icosahedron
There are many more stellations of the icosahedron, being the ones which do not come under "Miller's rules".
Some are also quite beautiful.
A selection, which various people have pointed out to me over the years, may be found here: https://www.steelpillow.com/polyhedra/icosa/lost/lost.html
Some are also quite beautiful.
A selection, which various people have pointed out to me over the years, may be found here: https://www.steelpillow.com/polyhedra/icosa/lost/lost.html
- Sun Aug 25, 2024 4:24 pm
- Forum: Polyhedra
- Topic: Edge-Transitive Polyhedra
- Replies: 13
- Views: 89826
Re: Edge-Transitive Polyhedra
These are fascinating to read about, and to examine the one thumbnail image which has been posted. They sound beautiful. But there is no polyhedron software which installs cleanly on my system and can view .off files equally cleanly. And Ulrich's image server is either broken or hates my system.
The ...
The ...
- Mon May 09, 2022 12:39 pm
- Forum: Stella Feature Requests
- Topic: Better rendering of infinite duals
- Replies: 9
- Views: 79123
Re: Better rendering of infinite duals
Looks good. Sorry to have fed you a red herring.
- Mon May 02, 2022 11:53 am
- Forum: Polyhedra
- Topic: How hard would it be to compute true filling?
- Replies: 8
- Views: 104187
Re: How hard would it be to compute true filling?
metachirality asked about regions suddenly flipping to a different density. I was trying to explain that using the conventional definition of a dense interior region, this cannot happen; as the polyhedron morphs, one region progressively gives way to another one of different density. A sudden flip ...
- Mon May 02, 2022 11:44 am
- Forum: Stella Feature Requests
- Topic: Better rendering of infinite duals
- Replies: 9
- Views: 79123
Re: Better rendering of infinite duals
I think there's only an issue when the centre of reciprocation lies in a facial plane (ie hemi faces). You'd get this issue even with convex polyhedra if you decide to put the centre of reciprocation on one of the faces. Nonconvex polyhedra work fine as long as they don't have hemi-faces.
Isn't ...
- Mon May 02, 2022 11:35 am
- Forum: Stella Forum
- Topic: Facetings of a polyhedron
- Replies: 2
- Views: 23031
Re: Facetings of a polyhedron
Thank you.
There seems to be a more or less "unlimited" option in there, excellent. Now I just need to get to grips with WINE.
Yes, "tidy" is a term I introduced, but the whole point of it is that it has no rigorous definition - it is a rag-bag of intuitive notions, which sometimes lead to ...
There seems to be a more or less "unlimited" option in there, excellent. Now I just need to get to grips with WINE.
Yes, "tidy" is a term I introduced, but the whole point of it is that it has no rigorous definition - it is a rag-bag of intuitive notions, which sometimes lead to ...
- Sun May 01, 2022 5:37 pm
- Forum: Stella Feature Requests
- Topic: Better rendering of infinite duals
- Replies: 9
- Views: 79123
Re: Better rendering of infinite duals
I recall discussing this many years ago.
The fundamental issue is that the "interior" of an infinite face is not defined. Polyhedral reciprocation is only equivalent to projective reciprocity for convex solids. Non-convexity introduces anomalies as to the filled-in bits of the face plane, and the ...
The fundamental issue is that the "interior" of an infinite face is not defined. Polyhedral reciprocation is only equivalent to projective reciprocity for convex solids. Non-convexity introduces anomalies as to the filled-in bits of the face plane, and the ...
- Sun May 01, 2022 5:24 pm
- Forum: Polyhedra
- Topic: How hard would it be to compute true filling?
- Replies: 8
- Views: 104187
Re: How hard would it be to compute true filling?
https://i.postimg.cc/9FMSRjrM/image.png
The issue here is, how do you define a "region"? When you pull apart the vertical and horizontal ends of the 4, are you pulling the horizontal away from the vertical, or are you pulling the vertical away from the horizontal? In each case, where does the ...