Search found 95 matches

by guy
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 ...
by guy
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 ...
by guy
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/
by guy
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 ...
by guy
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 ...
by guy
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.
by guy
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 ...
by guy
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
by guy
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 ...
by guy
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.
by guy
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 ...
by guy
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 ...
by guy
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 ...
by guy
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 ...
by guy
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 ...